The water environs of Okefenokee swamp: An application of static linear environ analysis

Ecological Modelling, 16 (1982) 1-50 Elsevier Scientific Publishing Company, Amsterdam--Printed in The Netherlands

1

T H E WATER ENVIRONS OF OKEFENOKEE SWAMP: A N APPLICATION OF STATIC LINEAR ENVIRON ANALYSIS

BERNARD C. PATTEN *

Department of Zoology and Institute of Ecology, University of Georgia, Athens, GA (U.S.A.)

JAMES H. MATIS

Institute of Statistics, Texas A and M University, College Station, TX (U.S.A.) (Accepted for publication 28 December 1981)

ABSTRACT Patten, B.C. and Matis, J.H., 1982. The water environs of Okefenokee Swamp: an application of static linear environ analysis. Ecol. Modelling, 16: 1-50. A static water budget model is constructed for the Okefenokee Swamp watershed (swamp plus upland portions) and decomposed into partition units called environs. Flow, storage, intercompartmental transfer and residence time analyses of these units are performed by environ analysis to determine qualitative and quantitative characteristics of Okefenokee ecosystem hydrology. The analysis indicates two relatively discrete hydrologic subsystems within the watershed. One consists of swamp surface water, driven by precipitation over the swamp. The other consists of upland surface water plus subsurface water in both swamp and uplands, whose source is precipitation on the uplands. Little exchange occurs between these two subsystems.

INTRODUCTION O k e f e n o k e e S w a m p is a n e x t e n s i v e p e a t l a n d in the U.S.A. s i t u a t e d o n the L o w e r A t l a n t i c C o a s t a l Plain of s o u t h e a s t e r n G e o r g i a , w i t h a s m a l l p o r t i o n in F l o r i d a . Its c l i m a t e is h u m i d s u b t r o p i c a l : h o t a n d wet d u r i n g M a y - S e p t e m b e r , w a r m a n d d r y in O c t o b e r - N o v e m b e r , cool a n d m o i s t in D e c e m b e r - F e b r u a r y , a n d w a r m a n d m o i s t d u r i n g M a r c h - A p r i l (Rykiel, 1977). Soils of the region are well l e a c h e d sands, w i t h acid p H , low

* University of Georgia, Contributions in Systems Ecology, No. 57, and Okefenokee Ecosystem Investigations, Publication No. 36. 0304-3800/82/0000-0000/$02.75

© 1982 Elsevier Scientific Publishing Company

concentrations of plant nutrients and shallow water tables. The regional vegetation Js Southeastern Evergreen Forest in which fire retards succession to mixed hardwoods (Monk, 1968). Pine culture is the major agroeconomic activity on non-swamp portions of the Okefenokee watershed, characterized by extensive stream channelization and roadside ditching to create xeric conditions favorable to the growth of, primarily, Pinus elliottii. These forestry practices alter the natural hydrology of the pine uplands, with unknown consequences for the swamp, which is both a National Wildlife Refuge (1937) and a National Wilderness Area (1974) in recognition of its significance to the American heritage. This paper concerns the hydrology of the Okefenokee swamp-uplands complex. It follows and is based on a first attempt to determine a water budget for the watershed (Rykiel, 1977, 1982). A static water balance model is formulated and decomposed into partition units by a new methodology for compartmental analysis, environ analysis (Matis and Patten, 1981). The Okefenokee watershed is depicted in Fig. 1. Its area is 3702 km 2, of which 1891 km 2 or 51% is occupied by Okefenokee Swamp; the remaining 1811 km 2 or 49% is pine uplands (Rykiel, 1982). * Elevation of the swamp averages 37 m above mean sea level, and the watershed boundary extends to 56 m on the western side. The topographic divide may or may not correspond to subsurface hydrologic divides, which are unknown. Therefore, precipitation outside the topographically delimited watershed may enter, or that falling inside may leave, as groundwater. In absence of specific knowledge to the contrary, it is assumed that the topographic divide functionally establishes the watershed boundary. Water exits the swamp in three drainages (Fig. 1): Suwannee River (74%) and Cypress Creek (which ultimately flows into the Suwannee, 14%) on the west and southwest, respectively, and St. Mary's River (12%) at the south on the eastern side (Blood, 1981). Divides for these drainages within the swamp are unknown. The swamp is a peat forming wetland. Its peat, up to 6600 years old (Cohen, 1973), is acidic and nutrient poor. Swamp vegetation is a mosaic of forests, shrub thickets and marshes (McCaffrey and Hamilton, 1978) molded in the general geologic, climatic and hydrologic setting by fire, forestry on the uplands and, within the swamp, lumbering and the construction of canals, boat trails and a dam (Hamilton, 1981). Three hydrologically significant recent anthropogenic modifications include: cutting the great transpiring cypress (Taxodium ascendens) forests during 1909-27 (Izlar, 1971),

* Newly determinedwatershed boundaries set these values at 1754 km2 or 46% swamp and 2027 km2 or 54% uplands, for a total watershedarea of 3781 km2 (Blood, 1981). The former values were used to derive the model, as described in the section entitled Materials.

Waycross

\

"omervil,e r

'

~uwannee R. Sill,~_-,-- i

"~--"

'-

....

-~--

"

,'amp

~OKEFENOKEE; :-~-~':~SW A M P -~--,.'z

Fargo

Moniac i

I

Watershed

Boundary

K,,

Swamp Area 0 6 L ! Approximate

12 Kms. j Scale

Fig. 1. The Okefenokee swamp-upland watershed. Most of the area of the uplands is in the northwest quadrant. The three output streams and the Suwannee River Sill are indicated.

dredging the 35 km Suwannee Canal during 1891-95 in a vain attempt to drain the swamp into the St. Mary's River (McQueen and Mizelle, 1926), and constructing the Suwannee River Sill in 1960 to retard fire. This sill, an earthen d a m situated where the Suwannee River leaves the swamp (Fig. 1), has raised water levels an average of 11 cm at Camp Cornelia across the swamp (Fig. 1), and reduced natural water level fluctuations 18-20% (Finn and Rykiel, 1979).

The combined effects of the sill and upland stream channelization and ditching, plus removal of the forests, all within the last century, probably make the Okefenokee a wetter swamp now than it has been over several millenia. The consequences cannot be foretold because too little is known about its basic hydrology. Systematic hydrologic studies have never been carried out on the uplands or in the swamp wilderness itself. Hence, there is a need to understand the water relationships which form the basis for the swamp's normal ecology, as well as its response to disturbances and management. The attempt here to clarify the macrohydrology of the Okefenokee watershed through a simple model represents an interim effort which hopefully will stimulate development of more definitive information in the future. A secondary purpose of the paper is to illustrate the utility of environ analysis in extracting a wealth of information from even a simple compartment model. MATERIALS: WATERSHED WATER BALANCE MODEL

Sediments beneath the Okefenokee Swamp overlie limestones which form a large artesian aquifer. This principal artesian aquifer is overlain by a thick layer of impermeable clay that separates it from a surface aquifer developed in the unconsolidated sands which comprise the regional surface deposit. Hydraulic interchange between the surface and deep aquifers is thought to be slight or non-existent because of this aquiclude. However, the principal artesian aquifer forms an extensive karst area to the west and northwest of the swamp, making it possible that rainfall in this region may recharge both the surface and deep aquifers. The piezometric surface of the artesian aquifer

Evapotranspiration Y~1 =1.58 II I Precipitation ~ z 1 =2.37 I

Evapotranspiration Y21 = 1.73

_-}

Surface I Upland I and Subsurface Storage ~ Flow l(no value)l f21=0714

_1 OwaO

I

' I: =

Precipitation z 2 =2.47

1 I. . . . . . . . . . .

'

t

Y2~ =0.0708 Deep Seepage

I

yg =1.38 Streamflow

'

y~ =0.0737 Deep Seepage

Fig. 2. Two compartment watershed water budget model of Rykiel (1977, 1982). Storage x~ is in units 109 m3. Inputs z, outputs y and the internal flow f are in 109 m3 y - i .

is 12 m below the surface of the swamp (Callahan, 1964), precluding any intrusion of deep water into the swamp. Springs, suggested to occur (Hopkins, 1947) and frequently purported by locals, must therefore derive from the surface sand aquifer or from minor aquifers within the aquiclude. Within this general setting, Rykiel (1977, 1982) produced the twocompartment watershed partition model shown in Fig. 2. In this figure z, f

HYDROLOGIC SUBMODEL Uplonds 1_ ATMOSPHERE CAPACITY / "

=

"~_._I_

l-'I-I I - - ~ _ . . . . . . . .

F....._

i CEPT,O.

OETEWA%. !

H"T , L ' OWl .~INFILTRATION

II

I

SWAMPSURFACEWATER~)"~t~"-J I

4"

,,

T!I

\\ SO,L

MOISTURE

SOIL

INTERFLOW BIOTA

ERODED SOIL

I(~~ I

L ITTER

------7 STREI ,MS ~

i _

"T ~ <

/_

~

i

\ ~

[

_

--

SUBSOIL k'-L ~SWAMP ~- ~GROUNDWATER ING FLOW I

I

I/

FLOW '( SWAMP SURFACE WATER

SHALLOW ~ GROUNDWATER

DEEP

i

_ wATER

DEEP ~

LATERAL

s

SUBSTRATE , w..~bSWAMP GROUNDWATER

I SEEPAGE / ~ ' - - - - ( SYSTEM LOSS Conceptual model of hydrologic processes in the Okefenokee watershed uplands

Fig.3. (Rykiel,1977,1982).

HYDROLOGIC SUBMODEL Swamp //~ CAPACITY/TI~I'"

I

I

', '.

I

I

I 1"1

-'"

~1

I SURFACE I

I I

INTERWATER I I CEPTION [___.~__.J DETENTION I

AREA A_ITHROUGHFALL~

I

/ STEMFLOW/

I I

L

~'9

I .L~ ~ }

ISLANDS .......

9

I I I

~I~

•

?,,./7~,~.,

ACTIVE LAYER WATER OVERLAND FLOW

PEAT BIOTA

SEDIMENT~_

EROOED PEAT

TRANSPORTA~

I

I

I

STREAMS

/-J CHANNEL"X~,"/ FLOW /

@ I

SYSTEM

LOSS

ROOT ZONE WATER

I BASEFLOW 7

PEAT

IPE"COL i'O | !

BASE FLOW~It

I DEEP PEAT WATER ._GEOLOGIC _ _ _ SUBSTRATE

SPRING SEEPS

SEEPAOE

LATERAL SYSTEM \

LOSS

/ LEAKAGE ]

x~¥;~7 ~

Fig. 4. Conceptual model of hydrologic processes in Okefenokee Swamp (Rykiel, 1977, 1982).

and y designate flows of water in units of 10 9 m 3 y - 1 and x* denotes water storage in the units 10 9 m 3. The areal basis for these numbers is the entire uplands or swamp. Processes are as follows, z] and z 2 represent annual precipitation inputs, f2~ is surface and subsurface transport of water from uplands (compartment 1) to the swamp (compartment 2). y~ and yg are

outputs from the watershed as evapotranspiration, y2 and y2 are additional outflows as deep seepage, and y3 represents output as streamflow. A storage value (x~) was provided only for the swamp. Sources of these data and associated assumptions are described in the cited references. Here the model and its data are accepted as a point of departure, noting the difficulties of quantification for such a large region. Rykiel (op. cit.) also formulated more elaborate conceptual hydrology models for both the uplands and swamp. His upland model (7 compartments) is reproduced in Fig. 3, and his swamp model (8 compartments) in Fig. 4. These conceptualizations exceed in complexity the available data for the Okefenokee watershed, but they provide a basis for disaggregating the Fig. 2 model into a slightly more detailed version whose quantification is possible with existing data. Accordingly, the quantitative model of Fig. 5 was produced by coalescing the Fig. 3 and 4 compartments and flows, as follows:

ET(x3(t)) y~ =1.6349

ET(Xl(t)) Y 1 =0.0793

'I z 1 =2.3647---~. I I I

I

SURFACE [ Er{x2{l~ ~, SAND/PEAY/y; =1.5007 =' AQUIFER t -

II

/

|

SF

• x l =0.0546

f31 =0.5238

~

PPT

z 3 =2 4700 I I I

x 3 =1.0722

~

I 3~= x~ =0.6454 ! |

~

q

f,2 =0.1804 |

I

/

kk ~

I

I *'=2 5646 ~ 4

. . . . . . . . . . . . . . . . . . y2 =0.0710 GW(x2(t))

S Y33=13662

" /1:~9 =0.0095

/y42 =0.0737 GW(x4(t))

I

|

'1

t

t

ETIx4{'I/ y~ =OO951

l Y4 =0.0138 SF ~

Fig. 5. Four compartment water budget model of the Okefenokee watershed. Compartments are: x~'=upland surface storage, x ~ = u p l a n d groundwater storage, x~'=swamp surface storage, x* = s w a m p subsurface storage. Inputs are: z~ = u p l a n d precipitation, z 2 = s w a m p precipitation. Outputs are y l = evapotranspiration, i --- 1. . . . . 4, y22 = deep seepage, y3 = sheet and stream flow, y2 =percolation, deep seepage and lateral leakage and y3 =baseflow. Intrasystem flows are: f~l =infiltration and percolation, f31 =channel and overland flow, fl 2 = baseflow and interflow, f32 = baseflow, f42 = lateral seepage, f43 = infiltration and percolation and f34 = u p w e l l i n g and water level rise. Storage units a r e 10 9 m 3, and input, output and internal flow units a r e 10 9 m 3 y - 1 . Areal basis is the entire watershed.

(1) Upland Surface Water. This compartment combines Interception, Surface Water Detention, Surface Depression and Streams from Fig. 3, with concomitant reduction of flows to one input z~ (precipitation), one output yl (evapotranspiration) and two outflows to other compartments, f2~ (infiltration and percolation) and f31 (overland and channel flow). (2) Upland Groundwater. Includes the Fig. 3 compartments Soil Moisture, Shallow Groundwater and Deep Groundwater, and flows reduced to two outputs, y2l (evapotranspiration) and y2 (deep seepage), f32 (baseflow) and f42 (lateral seepage). The flow f32, representing boundary baseflow where uplands meet swamp, is the only conceptual addition to Rykiel's model, which would appear as direct flows (not via Streams) in Fig. 3 from Shallow and Deep Groundwater compartments to Swamp Surface Water. (3) Swamp Surface Water. Islands and Streams in Fig. 4 are excluded as compartments in the Fig. 5 model. Islands are upland fragments within the swamp of negligible areal extent, and Streams as output conduits are regarded as functionally outside the watershed. This compartment thus incorporates only Interception and Surface Water Detention from Fig. 4. Associated flows include one input z 3 (precipitation), two watershed outputs y3l (evapotranspiration) and y3 (streamflow) and one intercompartmental outflow f43 (infiltration and percolation). (4) Swamp Subsurface Water. This compartment includes Active Layer Water, Root Zone Water, Deep Peat Water and Deep Groundwater from Fig. 4, with flows collapsed to three watershed outputs, y4~ (evapotranspiration), y42 (percolation, deep seepage and lateral leakage) and y43 (baseflow), and one outflow to another compartment f34 (water rise, unlabelled in Fig. 4). The storage values in Fig. 5 were derived as follows. Flooded areas were estimated from U.S. Geological Survey topographic maps to be 91 km 2 on the uplands and 1787 km 2 in the swamp (Pechmann et al., 1977). Corresponding non-flooded areas were 1720 km 2 uplands and 104 km 2 swamp. Depth of standing water in flooded areas was arbitrarily set at 0.6 m. Volume of Upland Surface Water was then computed as x~' =(0.091 X 10 9 m2)(0.6 m ) = 0.0546 X 109 m 3. Upland Groundwater volume was computed to an arbitrary soil depth of 3 m for the 1720 km 2 of unflooded area, and 2.4m ( 3 - 0 . 6 depth of storage) for the 91 km 2 of flooded area. Thus, (0.091 × 10 9 m2)(2.4m) + (1.720 X 10 9 m2)(3.0m) = 5.3784 X 10 9 m 3 soil volume. The field capacity of sandy loam is 0.12 v / v (Linsley et al., 1958), giving as the groundwater storage volume x~' --- (5.3784 X 10 9 m3)(0.12) = 0.6454 X 10 9 m 3. The volume of Swamp Surface Water, computed for an assumed average 0.6 m depth over the flooded swamp area of 1787 km 2, is x~ =(1.787 X 10 9 m2)(0.6m)= 1.0722 X 10 9 m 3. Rykiel (1977, p. 118) used 0.61 m and the entire swamp area of 1891 km 2 to obtain 1.15 X 10 9 m 3. Swamp Subsurface Storage was estimated for an assumed peat depth of

1.5 m underlain by a 1.0 m depth of sand. In flooded areas (0.6 m deep) d e p t h of peat was taken to be 1.5 - 0 . 6 = 0.9 m. Therefore, for the 1787 k m 2 of flooded and 104 k m 2 of unflooded swamp, the volume of peat is (1.787 X 109 m2)(0.9 m ) + (0.104 X 109 m2)(1.5 m ) = 1.7643 X 109 m 3. The field capacity of peat is 1.4 v / v (Linsley et al., 1958), giving a total volume of water held in peat in the swamp of (1.7643 X 109 m3)(1.4) = 2.4700 × 109 m 3. The 1 m depth of sand is distributed over the entire 1891 k m 2 of swamp area, giving 1.891 X 109 m 3 of sand. The field capacity of sand is 0.05 v / v , resulting in (1.891 × 109 m 3 ) ( 0 . 0 5 ) = 0 . 0 9 4 6 X 109 m 3 of water associated with sand in the swamp. The total Swamp Subsurface Storage is then x~ = (2.4700 X 10 9 m 3) -F (0.0946 X 10 9 m 3) = 2.5646 X 10 9 m 3. Rykiel (1977, p. 119), by a different method, estimated 0.532 X 10 9 m 3 for a 0 . 3 m hydrologically active peat depth, which is proportionally similar and, with the surface value above, yields the 1.682 X 10 9 m 3 total shown in Fig. 2. The flow values in Fig. 5 were derived in such a way as to preserve the essential relationships in Rykiel's two c o m p a r t m e n t model (Fig. 2). Thus, in units of 10 9 m 3 y - l , letting numbers in brackets denote the Fig. 2 or 5 models, zl[5 ] = 2.3647 - z~[2] = 2.3700; f3115] ( = 0.5238) -+-f3215] ( = 0.0095) +f4215] ( = 0.1804) = 0.7137 --f2112] = 0.7140y~[5] ( = 0.0793) +y2~[51 ( = 1.5007) --y~[2] ( = 1.5800); y~[5] ( = 0.0710) "--y~[2] ( = 0.0706); z315] = z2121 ( = 2.4700); y~[5] ( = 1.6349) +y~[5] ( = 0.0951) ---=y2~[2] ( = 1.7300); y215] = Y2212] ( = 0.0737); and y}[5l ( = 1.3662) +y315] ( = 0.0138) --y312] ( = 1.3800). The left h a n d side terms in these expressions were derived as follows: z~[5]. This value of 2.3647 X 109 m 3 y - I was reduced from 2.37 X 109 m 3 y - 1 in the Fig. 2 model to balance c o m p a r t m e n t 1. f3115]. Rykiel (1977, p. 80, p. 94) gives 26-year m e a n annual precipitation as 1284.9 m m y - l and 25-year mean annual streamflow as 283.9 m m m o n t h - l , or 22.1% of precipitation. H u n t (1972) reports regional runoff ranging 17-25% of precipitation, consistent with the 22.1% figure. R u n o f f was thus calculated as f3115] -- (0.221)z115 ] = (0.221)(2.37 × 10 9 m 3 y - l ) = 0.5238 X 10 9 m 3 y - 1 . f3215] and f4215]. The difference f2112] -f3~[5] = (0.714 X 109 m 3 y - l ) _ (0.5238 X 10 9 m 3 y - l ) = 0.1902 X 10 9 m 3 y - l is to be allocated to f3215] and f4215]. It is reasoned that upland baseflow to swamp surface water is a b o u n d a r y p h e n o m e n o n that, if it occurs at all, would be limited to the u p l a n d s - s w a m p interface and thus could involve very little of upland subsurface outflow. A n estimate of 5% is considered large. Thus, f3215] = (0.05)(0.1902 X 10 9 m 3 y-~) = 0.0095 X 1 0 9 m 3 y - L The remainder, lateral seepage, is f4215] = (0.1902 X 109 m 3 y - l ) _ (0.0095 X 109 m 3 y - l ) _ 0.1807 X 109 m 3 y - l , r e d u c e d to 0.1804 X 109 m 3 y - 1 to b a l a n c e c o m p a r t m e n t 4. y~[5] and Y2115]. F l o o d e d area (91 k m 2) of the uplands (1811 k m 2) is 5.02%. Tiffs fraction of y~[2]= 1.58 X 109 m 3 y - i is allocated to y~[5]=

10 0.0793 × 10 9 m 3 y - l , and the remainder toy~[5] = 1.5007 × 10 9 m 3 y - l . This surface-subsurface partition is consistent with values reported by Linsley et al. (1958) for sandy soil watersheds. y~[5]. The value of y215] = 0.0710 X 10 9 m 3 y-1 represents a negligible change from y~[2] = 0.0706 × 10 9 m 3 y-1 tO balance compartment 2. y~[5] and y115]. Flooded area (1787 km 2) of the swamp (1891 km 2) is 94.5%, which partitions y~[2] = 1.73 × 10 9 m 3 y-1 into y~[5] = 1.6349 × 10 9 m 3 y - i and y~[5] =0.0951 × 10 9 m 3 y - l . y315] and y315]. No information exists on surface flow versus baseflow of water exiting the swamp. What is known is that output is via the well-defined channels of the Suwannee and St. Mary's Rivers and Cypress Creek. Due to the high water holding capacity of peat, these streams may run dry where they leave the swamp and subsurface water can still be pumped from the peat virtually anywhere within the swamp (Hopkins, 1947). Thus, baseflow is arbitrarily assumed to contribute only 1% of streamflow outputs, resulting in a partition of y312] = 1.3800 × 10 9 m 3 y-1, with slight adjustment to balance the compartments, of y3315]= 1.3662 × 10 9 m 3 y-~ and y3 [5] = 0.0138 X 10 9 m 3 y-1. Surface and subsurface exchanges within the uplands and swamp were estimated as follows: f2115]. Evapotranspiration plus infiltration account for 90% of surface loss of precipitation of sandy soil monoculture watersheds (Swank and Douglass, 1977). Therefore, 0.9z115] =y~[5] +f2~[5], or 0.9(2.3647 × 10 9 m 3 y - l ) =(0.0793 × 109 m 3 y-l)+f2115], giving f2115] = 2.0489 × 109 m 3 y-1. This value was reduced to 2.0484 × l 0 9 m 3 y-~ to balance compartment 2. f~215]. All other flows into and out of compartments 1 and 2 are established at this point. Consequently, f~215]=0.2868 × 10 9 m 3 y - I for conservative balance. f3415]. Exchange from swamp subsurface to surface is arbitrarily assumed to be small, f3415] = 0.0010 × l 0 9 m 3 y-1. f4315]. With all other flows associated with compartments 3 and 4 already quantified, f4315] = 0.0032 × l 0 9 m 3 y - ! for balance. In summary, the quantitative model of Fig. 2 provided by Rykiel (1977, 1982) has been expanded along conceptual lines established by this same author (Figs. 3 and 4) in order to elaborate surface and subsurface water relationships in both the swamp and upland portions of the Okefenokee watershed. The data derivations above for the resulting Fig. 5 model reflect the inadequate state of knowledge about this critical ecosystem variable, underscore the need for further detailed study, and also place qualifications on results of the analysis to be performed below.

11 METHODS: ENVIRON ANALYSIS Patten (1978) defines an environ as the within system environment of each system component, inclusive of the component, and notes that every component has both an input environ and an output environ. The set of input environs of all a system's components forms a partition of the system, and the set of output environs likewise forms a second partition. Patten et al. (1976) and Patten (1978, 1982) should be consulted for theoretical background on the environ concept, and Patten and Auble (1981) for a treatment of the more familiar ecological niche as a restriction of the input environ. The methodology for implementing the environ concept, environ analysis (Matis and Patten, 1981), is related to deterministic (Finn, 1976, 1977, 1978) and stochastic (Barber, 1978a, b, 1979) i n p u t - o u t p u t flow analysis procedures for elaborating the flow origins of system outputs (input analysis) and the flow consequences of inputs (output analysis). These methods are descended from Leontief (1936, 1966) economic i n p u t - o u t p u t analysis, as introduced to ecology by H a n n o n (1973), and are reviewed by Barber et al. (1979). Environ analysis differs from previous flow analysis methods in providing storage partitions in addition to the usual flow partitions, accomplishing both by more straightforward formulations and computation procedures. In the present context, the water environs of each of the four compartments in the Fig. 5 model are to be described and analyzed. The subsequent outline of the methodology refers to formulations and equations as derived in Matis and Patten (1981). The compartment model represented by Fig. 5 can be described by systems of difference or differential equations, for example in the latter case, ;=l

j=O

jV=i

.....

j--O

j~i

where x~ is water stored in compartment i (m3); 2i is its first time derivative (m 3 y - l ) ; f~j and fji are flows from c o m p a r t m e n t j to i and i to j, respectively (m 3 y - l ) ; j = O signifies system environment; and n = 4 compartments. Letting z~ -~ fi0 and y~ ~ fo~ be environmental input and output, respectively, (1) can be written fji--Yi, "~i= Zi Af~ ~ fij-j=l j=l j~=i jv~i

i=

1 .....

n

(2)

Equations 1 and 2 depict the steady state compartment when 2 i = 2, = 0, 2i the second time derivative, and the compartment is static when these conditions prevail over an entire time interval of interest.

12

Figure5 is a static water budget for the Okefenokee watershed, and therefore its relationships can be formulated by a linear model. The normal parameterization is achieved by making each flow a function of its donor compartment, f,j = a i"j x j .• ~ :

a i,tj x j

Z i .q_

__

~

j=l

j#=i

=

~

2 i Jr-

a jt,i x i

j=0 j~i

"

aijx j

+

,,

aiixi

j=l j~i

= Z i -Jr-

aijxj,

j=l

or in matrix notation, ~: : A " X

+

(3)

Z

where

[i'

X 1

X=

all

• . .

A]! =

,

z 1 ,

II

n

n

aln

anl

2

~

t!

"""

ann

n

A n alternative linear parameterization is obtained by representing each flow as a function of its recipient compartment, fq = a~ixi: "~i :

a itj x i

--

--

Yi

j= 1

j~i

--

ajixj

--

j=0

j~J=i

t

-- a iix i

__ ~

/

a j i x j - - Yi

j=l j~i

n

-~-

--

ajixj--Yi,

i=

l,...,

n

j=0

j=/=i

or in matrix notation,

(4)

k = -A'x --y where x and 2 are as before, and all

A'=

I

" [a',

" " "

aln

Yl

y= ...

a:.

I,.

13 Note here the reverse orientation of the A' matrix elements. The logic flow of looking backward from outputs toward inputs is opposite the substance flow from inputs to outputs. In the static case, since 2 = 0, (3) and (4) can be written: (5)

0 =A"x* + z =A'x* +y

where x* represents the static storages in each compartment: x* = ( - A " ) - ' z

(6)

= (--A')-'y

The matrices ( --A")- 1 and ( - A ' ) - 1 apportion system inputs z and outputs y into steady state storages x*. For the Fig. 5 model, the matrices and vectors defined above are as follows: x*=

0.0546 0.6454

I

×109m 3

1.0711

2

'

2.5646 0.0793 1.5717 × Y---- 3.0011 0.1826

m3

10 9

Y-

2.36470 )< 109 m 3 y - l 2.4700 0

1

I -48.5623 A" = 37.5165 9.5934 0

0.4444 -3.1739 0.0147 0.2795

0 0 - 2.8020 0.0030

0 ] 0 ] y-1 0.0004 -0.0716

-48.5623 5.2528 0 0

3.1739 - 3.1739 0 0

0.4885 0.0089 -2.8020 0.0009

0 ] 0.0703 ] 1 0.0013 y -0.0716

A' =

I 0.0231 (_A,,)-1 = 0.2729 0.0806 1.0688

0.0032 0.3533 0.0131 1.3780

0 0 0.3569 0.0149

0 ] 0 0.0020 y 13.9685

0.0231 0.0382 0 0

0.0231 0.3532 0 0

0.0041 0.0079 0.3569 0.0046

0.0228 ] 0.3473 | 0.0062 [Y 13.9685 ]

(_A,)-I=

l

Environs are computed as follows. Let E," and E; be, respectively, input and output environs of compartment i --= 1,..., n, and let E;' = E ; ' / z i and E~ -= E;/yi be respective unit environs. The flows in these unit environs are

14

computed from

Fi" = A " D " ,

F i ' = D ' ( A ' ) T,

i = 1 ..... n

(7)

where D " and D" represent, respectively, diagonalized columns d " and d" of (--A") -1 and (--A') -l. Each element of F," represents the flow from the column compartment to the corresponding row compartment generated by one unit of input to compartment i. Each entry of F,' gives the flow from column to row compartment required to generate one unit of output from compartment i. The Fig. 5 model has two inputs z 1 and z3, and four outputs Yl ..... Y4. Therefore, it is appropriate to compute F~', F~' and F~.... , F~. These matrices are as follows (where 0 = 5.79 × 10-6): -

0 0 0 0

F; =

=

1.1213

0.1213

0.8662 0.2215 0

-0.8662 0.0040 0.0763

0 0 0 0

0 0 0

109 m 3 y-1 109 m 3 y - i

oo]

109 m 3 y - I

-0.0011

- 1.1213 1.1213 0 0

0.1213 - 1.1213 0 0

0 0 0

-0.1994 0.0251 0.1744 0

0.0216 -0.0251 0.0032 0.O003

0 0 -(1+0) 0

0.0030 0

×

109 m 3 y - I

0.1213 -0.1213 0 0

1.1021

0 0 0.0004 -0.0765

X

- 1.1213 0.1213 0 0

--1.1052 F~ =

0 0 -(1 +0) 0.0011

0 0 -0.2259 0.0002

0 0 0

× 109 m 3 y-~ 109m 3 y-l

0 0 0

°i]

0.1195 -- 1.1021

5.52 × 10 -5 0.9825

× 109m 3 y-l 109 m 3 y - 1

0 0 0.0003 -0.0003 0

0

0

0

--0.0175 0.0175

X

109 m 3 y 109 m 3 y - l

0 - (1 + 0)

109 m 3 y - i × 109 m 3 y - i

The diagonal elements of F~' represent total outflow from the corresponding column compartments; the other entries in each column specify outflows from that compartment to the others. Therefore, the column sums of F/', representing differences between total outflows and outflows to compart-

15

ments, denote outputs generated tO the system environment per unit of input z;. Similarly, the row sums of F~' represent inputs to the system environment per unit of output y;. These column or row sums over all environs can be arrayed in matrices W" = (wj") and W' = (w;j), where wj~' is t h e j t h column sum in F," and w'j is t h e j t h row sum in F;'. These elements have alternative interpretations as entry and exit probabilities (Matis and Patten, 1981, eq. 65): wfl is the probability that a unit of substance entering the system as z; will depart as yj, and w~jis the probability that a unit exiting as y; entered in zj. For the Fig. 5 model these matrices are: W" =

W' ----

0.0335 0.6647 0.2257 0.0761

).1778 0.9856

0 0 0 0

0 0 0.9989 0.0011

i]

0

0

0

0

0

0

0 0

0.8222 0.0144

0 0

× 10 9 m 3 y - t 109 m 3 y - l

3<

109 m 3 y - l 10 9 m 3 y-~

The number of transfers between compartments while a unit of substance is in a system can be computed as follows. Define p";j as the probability that material in compartment j = 1..... n at time t will be in compartment i - - 1 ..... n at time t + 1; and p~j as the probability that substance in j--- 1..... n at time t was in i = 1..... n at time t - 1. Let Q" and Q' be the matrices of these respective probabilities, calculated as:

Q"=(I+hA"),

Q'=(I+hA')

(8)

where I is the identity matrix, and h is a scalar chosen to make each diagonal element of Q" and Q' positive. Then Q" and Q' may be considered transition matrices of discrete time Markov chains, and h may be regarded as the number of discrete time points within a unit interval of time. For subsequent purposes the models that follow are parameterized with h ~ ~ , which corresponds to continuous time. Set the diagonal elements p~ and p~; equal to zero, and normalize each column of Q" and Q' by dividing its elements by the column sum to obtain matrices ~ " and ~'. From these form the matrices c3L" = ( I - ~ " ) - ',

~)L' = ( I - ~ ' ) - ' ,

63Lz = ~)L" + ~ '

(9)

(Matis and Patten, 1981, eq. 60) whose elements represent in the first case the expected number of times material in j = 1..... n at time t will visit c o m p a r t m e n t i = 1..... n before leaving the system, and in the second case the expected times substance in j at t has visited i since entering the system. The total expected visits to i = 1..... n of material in j = 1..... n at time t

16 while the material is in the system is ~)Lx. Variances associated with these expectations are computed from: U" = (2 ~)L~'- I ) 9L" - ~)L~',

U' = (29L~ - I ) % ' - OLd,

U x = U ' + U ''

(10) where 9L~' and 9L~ are diagonal matrices of 9L" and 9L', respectively, and 9L~' and %~ are matrices whose entries are the square of corresponding entries in 9U' and ~ ' , respectively. These matrices for the Fig. 5 model are as follows: 0 1.1213 0.1570 0 ~ , , = 0.8662 1.1213 0 0 (unitless) 0.2259 0.0367 1.00001 0.0054 1.00001 0.0765 0.0938 0.0011 0.1360 U"= 0.3260 0.1749 0.0707

0.1704 0.1360 0.0354 0.0890

0 0 5.83 X 0.0011

1.1213 9"6'= 0.1213 0 0

1.1213 1.1213 0 0

0.1994 0.0251 1.00001 0.0003

!.1360 .1360

0.1360 0.1360 0 0

0.2080 0.0305 5.80 X 10 -6 0.0003

U'=

~x=

Ux=

2.2426 0.9875 0.2259 0.0765 0.2720 0.4620 0.1749 0.0707

1.2783 2.2426 0.0367 0.0988 0.3064 0.2720 0.0354 0.0890

10 - 6

0.1994 0.0251 2.00002 0.0014

o

0 0.0054 5.83 X

1

(unitless)

10 - 6

1.1052 1.1022 (unitless) 0.0174 1.00001 0.1518 O. 1547 0.0171

1

(unitless)

5 . 8 0 X 10 - 6

1.1052 1.1022 (unitless) 0.0228 2.00002

0.2080 0.0305 1.16× 10 -s 0.0014

0.1518 0.1547 0.0225

] (unitless)

1.16 X 10 - s

Storage partitioning is achieved straightforwardly with the ( - - A " ) - l and matrices. Let x~. be the portion of x* which originates as input zj, and let x;'j be the fraction of x* which leaves the system as output yj, i, j = 1.... , n. Define Z and Y as diagonal matrices of z and y, respectively. Let X"(Z) and X'(Y) be matrices whose elements are the respective storage components x" U and x~j. Then:

(__4t)--1

X"(Z)=(-A")-'Z,

X'(Y)=(-A')-'Y

(ll)

17 For unit inputs or outputs, Z = Y = I, and

X"(I):(-A")

-~,

X'(I)=(-A')-'

(12)

Thus, ( - A " ) -1 and ( - A ' ) -1 specify the storage components x"ij and xij' scaled to unit values for the inputs zj and outputs yj, i, j = 1..... n. For the Fig. 5 water budget model, X " ( I ) and X ' ( I ) were given previously as ( - - A " ) - l and ( - A ' ) -1, respectively. The matrices X " ( Z ) and X ' ( Y ) are as follows:

X"(Z) =

X'(Y) =

0.0546 0.6454 0.1907 2.5279 0.0018 0.0030 0 0

0 0 0 0

0 0 0.8815 0.0367

0.0363 0.5553 0 0

0 0 0 0

X

0.0123 0.0237 1.0711 0.0139

109 m3 109 m 3 y - i

0.0042 0.0634 0.0011 2.5507

X

109 m3 109 m 3 y-1

N o t e that the residual units are years (y), which is also true for X " ( I ) and X'(I), which is consistent with the units for ( - A " ) -~ and ( - A ' ) -1. This leads to yet a third interpretation, residence time, for these inverse matrices. F r o m eq. 8 form the matrices

M" =(I-Q")

-~,

M'=(I-Q')-'

(13)

whose elements represent, in units t / h , the expected time material in c o m p a r t m e n t j at time t has resided in i since entering ( M " ) or will reside in i before leaving ( M ' ) the system. The time scales of M " and M ' can be adjusted to units of t by defining:

9]-(,, = h M " ,

a)]t' = hm ' ,

~JlLy~= aSqL"+ ~Jl~'

(14)

The-total expected time that substance in c o m p a r t m e n t j at time t will be in c o m p a r t m e n t i while it is within the system, given by the elements of aYt z, is the summation of future (9]L") and past (°-'At') residence times. Matis and Patten (1981) have shown the identity of ~L" and °"At' with the respective matrices ( - A " ) - l and ( - A ' ) -1 as follows:

9]L"

= hM" = h(I-Q,,)-I =h[I--(I+hA")]

6~,,

~- ( - - A " ) -1 ,

c)]L' -1

= hM' = h(I-O,)-i

(from 13)

=h[I--(I+hA')]-' °-.lit'

(from 8)

= (--A')-'

(15)

The corresponding variances of the residence times are computed by: V"=(29]t~'-I)~"-~',

V'=(2c)IL~-I)gL'-a)]t;,

Vz=V"+V' (16)

18 where ~)]L~' and °')]L~are diagonal matrices of ~ " and c)lL', respectively, and 9]L~' a n d ~L~ are matrices whose entries are the square of corresponding entries in GSqL"and ~)E', respectively. The residence time matrices 9~c" and 9L' for the Fig. 5 model have already been given as ( - A " ) - l and (--A')-1. The variance matrices are: V" =

V'=

V~=

0.0005 0.1184 0.0511 28.7216 0.0005 0.0255 0 0 0.0010 0.1439 0.0511 28.7216

1.39 X 10 -4 0.1248 0.0092 36.6469 0.0005 0.1248 0 0 0.0006 0.2496 0.0092 36.6469

0 0 0.1274 0.4154

1.73 X 10 -4 0.0055 0.1274 0.1299

] 0 0.0014 y2, 195.1190 0

1

0.0005 ] 0.1248 0.0044 y2 195.1190

1.73 X 10 -4 0.0055 0.2548 0.5453

1

0.0005 ]

0.1248 0.0058 y2 390.2380

1

In the next section the data which appear in the matrices of this section are organized and interpreted to yield a concept of surface and subsurface water relationships in the Okefenokee watershed. RESULTS The unit water environs E~', E i' and E~,..., E i of the Okefenokee watershed, as determined from the Fig. 5 model, are depicted in Figs. 6 and 7, respectively. As shown, environ analysis determines the input origins and output destinations of both flows and storages within the system. In this section flow relationships derived from the Fig. 5 model will be presented in terms of watershed input and output flows, intercompartmental flows and numbers of intercompartmental transfers. Storage relationships will be described in terms of storage partitions and residence times.

Input-output flow analysis." output environs There are three processes of water loss from the Fig. 5 system: evapotranspiration (ET), groundwater outflow (GW) and surface streamflow (SF). The output analysis question is, what inputs generate what proportions of these outputs? This information, lumped for all three processes, is contained in the W" matrix. In Tables I a - c these data are apportioned according to each individual process. The two left-hand columns in these

(a)

19

ET(t) 0.0335

PPT(t) 1.0

J o_ £1 ~t 1.12(0.37)

ET(t) 0.1230

0.0806 ~ 0.2215

.~_,-Q;3(0-.17 ; ]

0.8662

I

0.0002

0.1217. ET(t) 0.6347 ~ l - - t ~

0

0.0004

0.2729

1.0688

0.87(0.57)

0.08(0.26) 390d(5.0)

0.0763

100d(1.2)

0.0300 GW(t)

0.0307 GW(t)

ET(t) 0.0396

0.0058 SF(t)

(b) ET(t) 0.5442 I

L PPT(t) 1.0

0 3569 1.00(0.002) 130d (1.0)

0

0.0011

I I I

"~"~

0.4547 SF(t)

0.00000( 0.0149 O---e~

0

0

t............ 0

ET(t)

~-]0.001(0.03)

i

0.0004 GW(t)

v

0.0001 SF(t)

Fig. 6. Unit output environs (a) E~' and (b) E~'. Each diagram shows water flows (10 9 m 3 y ]) and storages (10 9 m 3) generated by one unit of input (10 9 m 3 y-1) at the bold arrow. Flows are associated with arrows, and storages appear as the upper number in each box. The middle numbers in each box represent, without parentheses, the expected number of future visits to that box of water presently entering the watershed via the compartment with the bold arrow, and within parentheses, associated standard deviations. Both these numbers are unitless. The bottom numbers in each box represent, without parentheses, the expected future residence time in that box of water presently entering the watershed via the bold arrow compartment, and within parentheses, associated coefficients of variation. The means are in hours (h), days (d) or years (y) and the coefficients of variation are unitless.

20 (a) ET(t) 1.0

0

t

I I

I I

0.0231

PPT(t) 1.0

1.12(0.37)

0

8d(1.0) 0

0"12100121£ 0 I

0.0382

0

0

-~-0

0 (b)

0

I...... I

I I

PPT(t) 1.0 ~

t ....

"l'

I I 1

0

I

0.0231

1.12(0.14)

0

8d(1.0) 1.1213

0

0.1213

0

0.3532 ET(t) GW(t) 1 . 0 , ~ I

I

1.12(0.37)

0

0

I ~'~--0

129d(1.0)

0

0

0

Fig. 7. Unit input environs (a) El, (b) E~, (c) E~ and (d) E,~. Each diagram shows water flows (10 9 1113y - l ) and storages (10 9 m 3) required to generate one unit of output (10 9 m 3 y - l ) al the bold arrow. Flows are associated with arrows, and storages appear as the upper number in each box. The middle numbers of each box represent, without parentheses, the mean numbe] of past visits to that box of water presently leaving the watershed from the compartment with

21 IET(t) ~SF(t) 1.0

(c) 0

+ 0.0041

PPT(t) 0.1778

0.20(0.46!36h(3.2)

-!

I °3569

0~.

Is

PPT(t) 0.8222

0.1744 JlO~-o-oo2)1 |-:30;';0; I

010251 0.0216 ~ 0.0079 0.03(0.1;; - 3 ~-~9-~)-

i

J

10,000006 ()00031t

1

I / 0.0046 I 0.0003 ~--JO.O 003~0702) -------i-~m. 0 1 4-0~/-7~.;.i

I \

0

0

0

(d) 0 I I I

PPT(t) II 0.9856

0"~---

t 0.0228 1.11(0.15) 8d(1.0) ~ 1.1021 0.1195 0.3473 1.10(0.39) . .127d(1.0) .....

t

0

o oo~o

I_ o oo~

PPT(t) 0.0144

I~,


I

2d(lO7) i ---..~, ° 0.0175

0.9825

O.O00001 13.9685 ~- 1.00(0.002) 14y(1.0)

'ET(t) .~ 1.0 ~SF(t) / GW(t)

-

the bold arrow, and within parentheses, associated standard deviations. Both these numbers are unitless. The bottom numbers in each box represent, without parentheses, the expected past residence time in that box of water presently exiting the watershed from the bold arrow compartment, and within parentheses, associated coefficients of variation. The means are in hours (h), days (d) or years (y), and the coefficients of variation are unitless.

22 TABLE I Proportions of W" matrix due to (a) evapotranspiration (process 1), (b) groundwater output (process 2) and (c) stream flow output (process 3) * (a) Evapotranspiration

Prob(y]lzj)

y~ y~ y~ y~ y

y][zj

Y~ z

z1=1

z3 = 1

zj =2.3647

23 =2.4700

0.0335 0.63472 0.1230 0.0396

0 0 0.54423 0.0006

0.0792 1,5009 0.29094 0.09365

0 0 1.34424 0.00155

0.0792 1.5009 1.63514 0.09515

0.83081'2'7

0.54481, 3,8

1.96466

1.34576

3.31036

(b) Groundwater outflow

yT[zj

Prob(y~21 zi)

y~ y~ y~ y~ y

2S z

zI= 1

z3 = 1

gl =2.3647

z 3:2.4700

0 0.03002 0 0.03072

0 0 0 0.00043

0 0.0709 0 0.07264

0 0 0 0.00104

0 0.0709 0 0.07364

0.06071&7

0.00041,3,8

0.14355

0.00105

0.14455

(c) Streamflow

yT[zj

Prob(yi3 [zj)

y~ y~ y~ y~ y

~ z

zl=l

z3=1

z1=2.3647

z3=2.4700

0 0 0.10272 0.00582

0 0 0.45473 0.00013

0 0 0.24294 0.01375

0 0 1.12314 0.00025

0 0 1.36604 0.01395

0.10851'2"7

0.45481,3, 8

0.25666

1.12336

1.37996

* Prob(y] [zj), which is unitless, represents output from compartment i = 1..... 4 by process k = 1, 2, 3 per unit inputj = 1, 3.y[lzj, in units of 109 m 3 y-l, is Prob(yiklzj) scaled to actual input values. Superscripts identify the data bases of text hypotheses having the same superscripts.

t a b l e s , l a b e l l e d P r o b ( y ~ [ z j ) , d e n o t e t h e o u t p u t f r o m c o m p a r t m e n t i--- 1 . . . . . 4 b y p r o c e s s k = 1 ( E T ) , 2 ( G W ) a n d 3 ( S F ) p e r u n i t i n p u t j = 1, 3. T h e s u m o f t h e s e c o l u m n s o v e r all t h r e e t a b l e s y i e l d s t h e first a n d t h i r d c o l u m n o f IV". T h e r e m a i n i n g c o l u m n s in T a b l e s I a - c r e p r e s e n t the s a m e i n f o r m a t i o n

23 scaled to actual precipitation inputs, the column to the right indicating total input (z I + z3) allocated to each corresponding output. Conclusions drawn from the data in these and subsequent tables will be expressed as hypotheses (H) to emphasize their tentative nature pending a more definitive data set and model. Data in the tables will be related to these hypotheses by means of numbered superscripts to identify the data bases for conclusions.

Evapotranspiration Evapotranspiration (ET) outputs y l, i = 1..... 4, in Fig. 5, are generally high compared to outflows Y7 (GW) and y3 (SF). The output environs (Fig. 6) verify ET as the major mechanism of water loss from the watershed. Most upland precipitation leaves as ET from the upland groundwater (0.6347) and swamp surface water (0.1230) compartments (Fig. 6a). More than half (0.5442 + 0.0006) of swamp precipitation leaves by ET, virtually all from the swamp surface water compartment (Fig. 6b). Most of swamp surface water ET is derived from swamp precipitation (0.5442 in Fig. 6b versus 0.1230 in Fig. 6a), whereas virtually all of swamp subsurface ET originates as precipitation on the uplands (0.6347 in Fig. 6a versus 0.0006 in Fig. 6b). The quantitative relationships corresponding to superscripted data in Table Ia are as follows. 1HI: 83% of upland precipitation, versus only 54% of swamp precipitation, is lost as watershed ET. 2Hl.l: 76% (0.6347/0.8308) of upland precipitation ET loss is from upland subsurface water, whereas 3H1.2: Virtually 100% (0.5442/0.5448) of swamp precipitation ET loss is from swamp surface water. 4'5~6H1.3: The proportions of upland and swamp precipitation in swamp ET are: 18% upland, 82% swamp in swamp surface ET4; 98% upland, 2% swamp in swamp subsurface ETS: and 59% upland and 41% swamp in total swamp ET 6. Groundwater output Outputs y22 and y4z in Fig. 5, and corresponding flows in Fig. 6, indicate that very little watershed precipitation exits the system as GW. Swamp precipitation lost by this means is negligible, and of upland precipitation so lost, half is in upland GW and half in swamp GW. Virtually all GW leaving the watershed originates as upland precipitation. Quantitative conclusions determined from Table Ib are as follows. ~H2: Only 6% of upland precipitation and 0.04% of swamp precipitation leave the watershed as GW loss. 2'3H2.1: GW losses of upland precipitation from the watershed occur 49%

24 from the uplands and 51% from the swamp2; all GW loss of swamp precipitation is as swamp GW 3. 4'5H2.2: The proportions of upland and swamp precipitation in swamp GW loss 4 and in total watershed GW loss 5 are 99 and 1%, respectively.

Streamflow Outputs y33 and y43 in Fig. 5, and corresponding partition values in Fig. 6, indicate that only a minor fraction of upland precipitation but almost half of swamp precipitation exit the watershed as SF. Most of upland precipitation and virtually all of swamp precipitation leaving as SF are from swamp surface water. Most of the water in SF is derived from swamp precipitation. Quantitative conclusions derived from Table Ic follow. ~H3:11% of upland precipitation leaves the watershed as SF loss, whereas 45% of swamp precipitation leaves as SF. 2H3.1: SF losses of upland precipitation are 95% from swamp surface water and only 5% from swamp subsurface water. 3H3.2: SF losses of swamp precipitation are virtually 100% from swamp surface water and only 0.02% from swamp subsurface water. 4'5'6H3.3: The proportions of upland and swamp precipitation in swamp streamflow are: 18% upland, 82% swamp in swamp surface SF4; 99% upland, 1% swamp in swamp subsurface SFS; and 19% upland, 81% swamp in total watershed (swamp) SF loss 6. The relative importance of the three output processes is given by comparing the Y y values in the corresponding z i = 1 columns, i = 1, 3, of Tables Ia-c. H4: Water loss from both uplands and swamp, in descending order of importance by processes, is ET > SF > GW. 7H4.1: 83% of upland precipitation is lost as ET, 11% as SF and 6% as GW. 8H4.2: 54% of swamp precipitation is lost as ET, 45% as SF and much less than 1% as GW.

Input-output flow analysis: input environs The input analysis question is: what are the input origins of the watershed outputs? The output processes need not be distinguished for this determination. The IV' matrix contains the necessary information, which is displayed in the unit input environ diagrams of Fig. 7. The following conclusions are derived from W', whose c o l u m n s j represent input sources zj (only z I and z 3 are non-zero), whose rows i denote output distinctions y;, i = 1..... 4, and whose entries are Prob(zj[y i) indicating the origins of outputs. H5: The origin of all water lost from the uplands is, obvious!y, upland

25

precipitation (W~ = 1 and W~l = 1, indicating z I as the source of bothy~ and Y2, respectively). H6: Water lost from the swamp surface originates predominantly as swamp surface precipitation (0.8222 versus 0.1778), whereas water lost from the swamp subsurface originates almost exclusively with upland (0.9856) rather than swamp (0.0144) precipitation. Thus, H6.1: Only 18% of water lost from the swamp surface has its origin in upland precipitation, while 82% of such loss originates as swamp precipitation; and H6.2: Water lost from the swamp subsurface has as its origin 99% upland and 1% swamp precipitation. Therefore, most of the swamp surface water exiting the watershed by ET, GW or SF processes is derived from swamp precipitation, whereas swamp subsurface water which leaves originates almost exclusively with precipitation on the uplands.

Intercompartmental flow analysis: output environs Within system flows between the compartments generated by unit precipitation inputs appear in the F(' and F~' matrices, and are depicted in Fig. 6. These data are entered in the first two columns of Table II, and corresponding values scaled to absolute inputs appear in the remaining columns. The

T A B L E II Intrasystem flow data from unit matrices ~", j = 1, 3 * f, klunit zj

f, klzj

~ z

zI= 1

z3=l

z I =2.3647

z 3 =2.4700

f21 f31

0.86623`4 0.22153`4

0 0

2.0483 0.5238

0 0

2.0483 0.5238

fl2 f32 f42

0.12133'5 0.00403'3 0.07633.5

0 0 0

0.2868 0.0095 0.1802

0 0 0

0.2868 0.0095 0.1802

f43

0"00023'6

0'00116

0"00057

0"00277

0"00327

f34

0.00043"6

0.0000066

0"00098

0'00001s

0"000918

Y~f,k

1"28991

0.0011061

3.05002

0.002712

3.052712

* f/klunit zj represents unitless within system flows from compartment k = 1..... 4 to i = 1..... 4 generated by unit inputs zj. f,k Izj columns indicate the same flows, with units 10 9 m 3 y - i , scaled to actual input values. Superscripts refer to text hypotheses.

26 general conclusions are that virtually all intercompartmental transfers are of water which originates as upland precipitation, swamp surface to subsurface movement involves mainly water from swamp precipitation, but swamp subsurface to surface transfer is almost exclusively of water which originates in upland precipitation. More specific conclusions derived from Table II are as follows. H7: Most water exchanged between compartments within the system originates with upland precipitation. ~H7.1: One unit of precipitation on the uplands generates 1.29 units of intrasystem flows, whereas one unit of swamp precipitation generates only 0.001 units of intercompartmental exchange. 2H7.2: Almost all within system exchange involves upland precipitation water; less than 0.09% of such exchange is of water derived from swamp precipitation (the only two flows are f43 and f34). 3H8: One unit of upland precipitation generates intrasystem compartment outflows as follows: upland surface water 1.09 (0.8862+0.2215) units, upland groundwater 0.20 units, swamp surface water 0.0002 units and swamp subsurface water 0.0004 units. 4H8.1: 80% of upland precipitation which is transferred within the watershed infiltrates and percolates to upland groundwater; only 20% moves by stream channel or overland flow to swamp surface water. 5H8.2: 60% of intrasystem upland groundwater outflow is returned to upland surface water, and 38% moves laterally to swamp groundwater; only 2% is transferred by baseflow to swamp surface water. H9: Exchange between swamp surface and subsurface water is extremely small and mainly involves water originating as swamp precipitation. 6H9.1: Per unit input: upland precipitation generates only 0.0002 units of swamp surface to subsurface flow, and 0.0004 units of subsurface to surface flow; swamp precipitation generates 0.0011 units of surface to subsurface flow, and only 0.000006 units of subsurface to surface flow. 7H9.2: 84% of swamp surface to subsurface flow originates as swamp precipitation and only 16% as upland precipitation. 8H9.3: 99% of swamp subsurface to surface flow has upland precipitation origin, and only 1% is derived from swamp precipitation.

lntercompartmental flow analysis: input environs Within system flows responsible for the production of unit outputs are contained in the F{ .... , F~ matrices. These flows appear in the unit output environ diagrams (Fig. 7) and in the first four columns of Table III. Corresponding values scaled to the actual outputs are in the remaining table columns. These data indicate that most intercompartmental exchange of

0.12133 0.12133 0 0 0 0 0 0.24261

0.12134 1.12134 0 0 0 0 0 1-24261

0.02165 0.02515 0.17445 0.00325 0.00035 0.00035 0.0000065 0.2249061

0.11956 1.10216 0.00306 0.000066 0.0000066 0.98256 0.01756 2-2246661

0.00967 0.00968 0 0 0 0 0 0-01922

0.19066 1.76238 0 0 0 0 0 1.95292

y2 = 1.5717 0.06487 0.07538 0.52349 0.00969 0.00099 0.0009 0.000018 0.6749182

y3----3.0011

0.02187 0.20128 0.0005 0.00001 0.000001 0.17941° 0.0032 l° 0.4061112

y4 =0.1826 0.2868 2.0484 0.52399 0.009619 0.0009019 0.18031° 0.003218 I° 3.0531292

Y"Y

*~, J unit yj denotes unitless within system flows from compartment k = 1. . . . . 4 to i = 1. . . . . 4 which produce unit outputs y~. f,~ ]yj columns represent the same flows in units of 10 9 m 3 y 1 scaled to actual input values. Superscripts refer to text hypotheses.

fl2 f21 fal f32 f34 f42 f43 fik

y4~-I

yl =-0.0793

y3=l

yl=l

Y2=l

f/k l Yj

f,k Iunit Yj

Intrasystem flow data from unit matrices ~', j = 1. . . . . 4 *

TABLE III

---.,I

28 water is associated with subsurface rather than surface outputs. The principal quantitative conclusions derived from Table III follow. H10: More water exchanged between compartments within the system is associated with groundwater outputs than with surface water outputs. ~H10.1: Internal system flows supporting unit outputs are: upland surface output 0.24, upland groundwater output 1.24, swamp surface output 0.22, and swamp subsurface output 2.22 2H10.2: The percentages of total intrasystem flows responsible for generating system outputs are: upland surface 0.63% (0.0192/3.0532), upland subsurface 64%, swamp surface 22% and swamp subsurface 13%. Table III contains numerous other specific relationships between intrasystem flows and outputs which, for brevity, are left to the reader to explore. To aid this process, additional superscripts (3-10) are included in the table to identify sets of numbers in which these relationships are implicit.

Number of intercompartmental transfers In a system with more complex internal connections than the Fig. 5 model, the number of intercompartmental transfers indicates the importance of cycling versus straight flow through in the system structure. The only flow cycles in the Fig. 5 model are surface-subsurface exchange in both upland and swamp subsystems, with very low rates in the latter case (a~'3, a ~ in matrix A", and a~3 , a~4 in matrix A'). Thus, the Fig. 5 model tends to be a flow through system with not much detention due to cycling between compartments. The number of intercompartmental transfers and associated variances serve to clarify principal routes of water flow through the system.

Future intercompartmental transfers: output environs The 9L" matrix gives the expected number of future visits to compartment i = 1,..., 4 while in the system, of a unit of water entering the system via c o m p a r t m e n t j = 1.... , 4 at time t, counting the initial entry as one visit toj. Associated variances appear in the U" matrix. Means and standard deviations, (U") ~/2, associated with compartments 1 and 3 appear in Fig. 6 as the middle set of numbers (mean (standard deviation)) in each box. The principal conclusions to be drawn are as follows. H11: Water tends to restricted rather than diverse movement within the Okefenokee watershed. H11.1: The numbers of future intercompartmental transfers within the system are small. These numbers are the column sums minus 1.0 of each 9L" column: 1.29 for upland surface water, 0.41 for upland groundwater, 0.001 for swamp surface water and 0.006 for swamp subsurface water, with respective standard deviations 0.8412, 0.6564, 0.0328 and 0.0736.

29 Hl l.2: The cycles between compartments 1 and 2, and 3 and 4 are of negligible quantitative significance. The numbers of future returns of water in each compartment back to that compartment, given by each principal diagonal element of % " , minus 1.0, average only 0.12 transfers for upland compartments, and 10 -5 transfers for swamp compartments. H11.3: Uncertainty in the network is low. Standard deviations are generally small (Fig. 6), the maximum value associated with a given intercompartmental transfer being only 0.57 transfers, corresponding to variance u~'1 = 0.3260 in the U" matrix.

Past intercompartmental transfers: input environs The matrix % ' gives the expected number of past visits to compartment i-- 1..... 4, since in the system, of water leaving the system from compartment j = 1..... 4 at time t, counting the terminal exit as one visit to j. Corresponding variances are given in the U' matrix. These means and standard deviations, (U') 1/2, are shown in Fig. 7 as the middle numbers (mean (standard deviation)) in each box. Hl l.4: The numbers of past intercompartmental transfers within the system are small, and greatest for the subsurface compartments. Summing the columns of % ' and subtracting 1.0 in each case, the average number of past returns is 0.24 for upland surface water, 1.24 for upland groundwater, 0.22 for swamp surface water and 2.22 for swamp subsurface water. H11.5: The surface-subsurface cycles are quantitatively negligible. Subtracting 1.0 from the principal diagonal elements of %', the number of times water in a compartment was previously in that compartment is, as in H 11.2, 0.12 for upland compartments and 10-5 for swamp compartments. H11.6: Small network uncertainty is indicated by small standard deviations. The maximum value associated with a given intercompartmental transfer is only 0.46 (Fig. 7c), corresponding to u~3 = 0.2080 in the U' variance matrix.

Total intercompartmental transfers The %y~ and Uz~ matrices give expected values and variances, respectively, for the total number of visits to compartment i = 1,..., 4, while in the system, of water in c o m p a r t m e n t j = 1..... 4 at time t, counting presence i n j as one visit. H11.7: The total number of intercompartmental transfers of water within the system is small. Subtracting 1.0 from each column sum for %~, the mean number of total transfers is 2.53 for upland surface water, 2.66 for upland groundwater, 1.23 for swamp surface water and 3.23 for swamp subsurface water. Hl l.8: The surface-subsurface cycles have minor quantitative signifi-

30 cance. Subtracting 1.0 from each principal diagonal element of qgL~, the total number of times water in a compartment has visited or will visit that compartment is 1.24 for upland compartments and 1.00002 for swamp compartments. Hl l.9: Standard deviations for total numbers of intercompartmental transfers are small. The maximum value associated with a particular transfer is 0.68, corresponding to (u21)~ = 0.4620 in the U~ variance matrix. Thus, the Fig. 5 model yields the general conclusion that water movement is tightly constrained within the Okefenokee s w a m p - u p l a n d system.

Input-output storage analysis: output environs The output analysis question with respect to compartment storages is, how are inputs partitioned into components of storage? As indicated in eqs. 11 and 12, this information is contained in the (--A") -l and X"(Z) matrices. The first and third columns of these matrices are generated by z I and z 3, and the normalized values in ( - A " ) - 1 appear as the upper numbers in the boxes of Fig. 6. Conclusions from the data in (--A") -1 and X"(Z) are as follows. H12: From the sums of columns 1 and 3 in ( - A " ) -1, one unit of upland precipitation generates 1.45 units of water stored in the watershed; one unit of swamp precipitation generates only 0.37 units of watershed (i.e. swamp) storage. H 13: Upland precipitation generates primarily subsurface storage, particularly swamp subsurface water. From the ratios of ( - A " ) -~ column 1 elements to the column sum, percentages of total storage due to upland precipitation in each compartment are: upland surface storage less than 2%, upland subsurface storage 19%, swamp surface storage 6% and swamp subsurface storage 74%. H 14: Swamp precipitation generates primarily surface storage. From the ratios of (--A") -~ column 3 elements to the column sum, percentages of total storage due to swamp precipitation in each compartment are: swamp surface storage 96% and swamp subsurface storage 4%. H15: The composition of swamp surface water in terms of input origins is: 18% derived from upland precipitation and 82% derived from swamp precipitation (same as H6.1, here computed as the ratios of X"(Z) row 3 elements to the row sum). H16: The composition of swamp subsurface water in terms of input origins is: 99% derived from upland precipitation and only 1% derived from swamp precipitation (same as H6.2, here computed as the ratios of X"(Z) row 4 elements to the row sum). Thus, upland precipitation accounts for significantly more watershed storage than swamp precipitation, particularly subsurface storage, and especially swamp subsurface storage. Swamp precipitation, on the other hand,

31 generates principally surface storage. Swamp surface water is largely composed of swamp precipitation, but swamp subsurface water originates almost exclusively with precipitation on the uplands.

Input-output storage analysis: input environs The input analysis question in relation to compartment storages is, what component of each storage contributes to each system output? As established in eqs. 11 and 12, the matrices (--A') -1 and X'(Y) represent this storage partition information. The upper numbers in the boxes of Fig. 7 are the ( - A ' ) - 1 elements. Conclusions follow. H17: From the column sums of ( - A ' ) 1, total system storages required to generate one unit of each output are: upland surface output 0.06, upland subsurface output 0.38, swamp surface output 0.37 and swamp subsurface output 14.34 units. H18: The composition of each system output with respect to storage origins, determined as ratios of column elements to corresponding column sums in ( - A ' ) -1, is as follows: H18.1: Upland surface output is 38% upland surface water and 62% upland groundwater. H18.2: Upland groundwater output is 6% upland surface water and 94% upland groundwater. H18.3: Swamp surface output consists of 1% upland surface water, 2% upland groundwater, 96% swamp surface water and 1% swamp subsurface water. H18.4: Swamp subsurface output consists of 0.2% upland surface water, 2% upland groundwater, 0.04% swamp surface water and 97% swamp subsurface water. H19: The fate of each compartmental storage in terms of output destinations, computed as ratios of row elements to corresponding row sums in X'(Y), is as follows: H19.1: Upland surface water storage is destined to leave the watershed in the following outputs: upland surface 3%, upland groundwater 66%, swamp surface 23% and swamp subsurface 9%. H19.2: Upland subsurface water storage is destined to leave the watershed in the following outputs: upland surface 0.46%, upland subsurface 86%, swamp surface 4% and swamp subsurface 10%. H19.3: Swamp surface water storage is destined to leave the watershed in the following outputs: swamp surface 99.9% and swamp subsurface 0.10%. H19.4: Swamp subsurface water storage is destined to leave the watershed in the following outputs: swamp surface 0.5% and swamp subsurface 99.5%. Principal generalizations are thus: swamp subsurface storage is great per

32 unit of subsurface output, whereas system storage levels are otherwise small per unit of the other outputs. Compositionally, upland surface output is two-thirds groundwater, where outputs from the other compartments are derived predominantly from storages in those compartments. Regarding output destinations, two-thirds of upland surface water exits as upland groundwater, whereas most of upland groundwater leaves as such, and virtually all of swamp surface and subsurface storages depart as outputs from these same compartments. Residence times

As developed in the section on Methods, the total time a unit of substance resides in a compartmental system can be decomposed into a future and a past. Environ analysis permits computation of both expectations and variances for these residence time components as well as for total time in the system, or any specifiable subsystem. In the following sections, residence times of water in individual compartments; in the uplands, swamp, surface water and subsurface water subsystems; and in the entire watershed will be analyzed. Future residence times: output environs The ( - A " ) - ~ and V" matrices give expectations and variances, respectively, for the future residence times in compartment i = 1,..., 4 of water entering the system via compartment j = 1,..., 4 at time t. The respective units are y and y2. These data are presented in the first four rows of Table IVa, with variable time scales for convenient interpretation, and with coefficients of variation (standard deviation/mean) listed instead of variances. Note that the coefficients of variation are 1.0 on the principal diagonal. In addition, data for subsystems formed from different compartment combinations, and for the whole system, are entered. The individual compartment values in the first and third columns are also displayed (mean (coefficient of variation)) as the bottom set of numbers in the boxes of Fig. 6. The following conclusions are derived from Table IVa, with superscripts referring to supporting data in each case. 1H20: Upland precipitation has a longer and relatively more variable future in the watershed than swamp precipitation. Mean future residence time of upland precipitation is four times greater than swamp precipitation (1.45 y versus 135.71 d), and the coefficient of variation is almost twice as great (3.72 versus 1.98). H21: Upland precipitation has a longer and relatively more variable future as subsurface water than as surface water, 2,3 whereas swamp precipitation has a longer but relatively less variable future as surface water than as

33 subsurface water. 4'5 The numerical data supporting these conclusions are identified in Table IVa by the indicated superscripts. 6H22: The watershed future of upland precipitation is longer and considerably more variable in the swamp than in the uplands. Future residence time of upland precipitation in the swamp is four times longer than in the uplands (1.15 y versus 108.04 d), and the associated coefficient of variation is also four times greater (4.67 versus 1.16). H23: Water entering swamp surface water has the shortest future, and that entering swamp subsurface water the longest future in the watershed. Water entering upland surface versus subsurface compartments has comparable future durations and variabilities. 7H23.1: The watershed future residence time of water introduced to the swamp surface component is only 135.71 d, with a coefficient of variation of 1.98. The future residence time of water entering the swamp subsurface compartment is 13.97 y, with a smaller coefficient of variation, 1.00, than that for swamp surface water. 8H23.2: Water entering the upland groundwater compartment will remain within the system somewhat longer (1.75 y) than that entering upland surface water (1.45 y), but with somewhat smaller variability (coefficient of variation 3.47 versus 3.72 for the surface compartment). H24: Water entering upland surface water is labile with moderate variability, that introduced into upland groundwater or swamp surface water is of intermediate mobility a n d slightly smaller variability and that entering the swamp subsurface compartment is immobile and also of slightly smaller variability. 9H24.1: Water entering the system as upland surface water will be upland surface water for a total of only 8.43 d, with 1.00 coefficient of variation. 1°H24.2: Water introduced into upland groundwater or swamp surface water has future identity times of 128.95 d and 130.27 d, respectively, with coefficients of variation of unity in both cases. ~H24.3: Water entering the swamp subsurface compartment will remain therein for 13.97 y, with a coefficient of variation of unity also. ~2H25: Subsurface water transferring to the surface has short futures in the receiving surface compartments: swamp subsurface water will reside only 16.64 h in swamp surface water, with a high coefficient of variation (19.68); upland groundwater will reside only 28.03 h in upland surface water, and only 4.78 d in swamp surface water, both with relatively high coefficients of variation of 3.69 and 7.32, respectively. ~3H26: Water entering the uplands has a four times longer future in the swamp than in the uplands (1.15 y versus 108.04 d for surface water, and 1.39 y versus 130.12 d for groundwater). 14H27: The fraction of future residence time in the watershed that water

37.85 d (2.19) 4 1.34 y (4.00) 4

x~' + x~' x~ + x,~

1.45 y (3.72) 1'8'14

8.43 d (1.00) 4 13.94 d (4.18) 6 0 (oo) 0 (o¢)

22.37 d (2.63) 6 0 (oo)

x~" x~ x~ x,~

x~' + x~ x~ + x~

(b) Past residence times

Y, x*

108.04 d (1.16) 6"13 1.15 y (4.67) 6'13

x]~+ x~' x~'+ x~

d (1.26) 2 d (2.81) 3 d (5.01) 3

d (1.00) 2"9'14

8.43 99.61 29.42 390.11

x~" x~ x~' x,~

(a) Future residence times

x~(t)

h d d y

(3.69) 12 (1.00) 1°'14 (7.32) 12 (4.39)

(1.00) 7 (1.00) 5 (oo) (~)

137.39 d (0.94) 7 0 (oo)

8.43. d 128.95 d 0 0

i.75 y (3.47) 8'14

5.95 d (5.91) 1.73 y (3.50)

130.12 d (0.99) 13 1.39 y (4.35) 13

28.03 128.95 4.78 1.38

x~(t)

(6.28) 1° (1.40) 1°

h (3.22) 8 d (9.41) 8 d (1.00) 5,9 h (77.51) 8 4.38 d 131.95 d

35.92 2.88 130.27 40.30

135.71 d (1.98) 1'7'14

130.27 d (1.00) 5 5.44 d (43.26) 5

0 (oo) 135.71 d (1.98)

0 (oo) 0 (~) 130.27 d (1.00) 5'1°'14 5.44 d (43.26) 5

x~(t)

d d d y 135.09 d 13.97 y

8.32 126.76 2.26 13.97

13.97 y

16.64 h 13.97 y

0 13.97 y

0 0 16.64 h 13.97 y

x,~(t)

(0.96) 16 (1.00) 16

(0.99) 12 (1.02) 13 (10.67) 14 (1.00) TM

(1.00) TM

(19.68) (1.00)

(~) (1.00)

(oo) (~) (19.68) 12 (1.00) 11'14

Future residence time data derived from matrices ( - A " ) - 1 and V"(a) a, past residence time data derived from matrices ( - A ' ) - l and V' (b) b and total residence time data derived from 6)E~ and V~ (c) b

TABLE IV

x~" + x~' x~ + x~

d d d y

(0.93) (0,71) 2 (7.32) 3 (4.39)

2.13 y (2.86) 1

14.38 d (2.51) 1° 2.09 y (2.91) l°

267.51 d (0.68) 5 1.39 y (4.35) 5

9.60 257.91 4.78 1.38

137.39 d (1.00) 2"5

8.43 d (0.98) 128.95 d (1.00) (1.37) z'~

272.04 d

(1.20) 1

262.04 d (0.70) 8 10.00 d (27.09) 8

(6.29) 6 (1.22) 6

h (3.21) d (9.39) d (0.71) 2 d (37.87) 12

4.38 d 267.66 d

35.92 2.88 260.54 7.12

136.33 d

131.77 d (0.99) t' 4.56 d (29.44) ll

d d d y

28.32 y

11.28 d 28.28 y

135.09 d 27.95 y

8.32 126.76 2.96 27.94

14.34 y

10.59 d 14.32 y

(0.02) 1

(0.02) 11

(2.57) 11

(0.96) 7 (0.02) 7

(0.98) (1.02) (9.40) 3'12 (0.02) z

(0.97) 3`3

(2.41)" (0.98) 17

a Numbers without parentheses, derived from ( - A " ) - 1 , represent expected future residence times (h = hours, d = days, y = years) in row compartments i=l,..., 4, subsystems defined as combinations of compartments, and the entire system, of water entering column compartments j = 1. . . . . 4 at time t. Numbers within parentheses represent unitless coefficients of variation (standard d e v i a t i o n / m e a n ) , where standard deviations were computed as square roots of V" elements. Superscripts refer to text hypotheses, b Format and units same as (a), with means without parentheses and coefficients of variation within parentheses. Superscripts refer to text hypotheses.

1.51 y (0.64) 1

46.28 d (1.80) 9 1.38 y (0.67) 9

x'~+x,~

22 x*

130.41 d (1.07) 4 1.15 y (0.76) 4

x~' + x~

(0.68) 2 (1.22) (2.80) 3 (0.79)

16.86 113.55 29.42 390.11

x~' x~' x~' x,~

d d d d

22.37 d (2.63) 1'2'4

22 x*

(c) Total residence times

8.43 d (0.98) 13.94 d (4.18)

x'~+x~ x~+x'~

36 enter!ng each compartment will spend in that compartment increases from uplands to swamp and surface to subsurface compartments: upland surface water 1.6% (8.43 d/1.45 y), upland groundwater 20% (128.95 d/1.75 y), swamp surface water 96% (130.27 d/135.71 d) and swamp subsurface water virtually 100% (13.9685 y/13.9704 y). These conclusions do not exhaust the relationships implicit in Table IVa, but they capture the most salient ones which support the following generalizations. Regarding precipitation, upland precipitation has a longer, relatively more variable watershed future than swamp precipitation; upland precipitation has a longer and relatively more variable future as groundwater than as surface water; swamp precipitation has a longer, relatively less variable future as surface water than as subsurface water; upland precipitation will reside longer in subsurface than in surface storage, whereas swamp precipitation will reside longer in surface than in subsurface storage; and the future of upland precipitation is longer and more variable in the swamp than in the uplands. Regarding water entering different storages, swamp surface water has the shortest watershed future, and swamp subsurface water the longest future, upland surface water is relatively labile, while swamp subsurface water is relatively immobile; subsurface water transferred to surface compartments has short futures in those compartments; upland water has a considerably longer future in the swamp than in the uplands; and, finally, water entering the compartments will spend increasing fractions of its future residence times within those compartments in ascending sequence from surface to subsurface and uplands to swamp. Past residence times: input environs The matrices ( - A ' ) - 1 and II' give the means and variances, respectively, of past residence times in compartment i - - 1 ..... 4 of water leaving the system from compartment j - 1,..., 4 at time t. These data appear in the first four rows of Table IVb, with coefficients of variation given rather than variances, and with time units variable as in Table IVa to aid interpretation. Data for the subsystems previously considered, and for the entire system, are also included in the table. In addition, the individual compartment values (mean (coefficient of variation)) are also shown as the bottom numbers in the boxes of Fig. 7. Conclusions formulated from Table IVb are as follows. H28: Water leaving the system as upland surface, upland subsurface or swamp surface outputs has relatively short and small variability histories within the watershed, whereas water exiting from the swamp subsurface has resided in the system for a relatively long and invariable period of time. ~H28.1: Water leaving the system from the upland surface water compartment has been in the watershed only 22.37 d, with a coefficient of variation of 2.63.

37 2H28.2: Water exiting the system from upland subsurface and swamp surface compartments has resided in the system 137.39 and 136.33 d, respectively, with associated coefficients of variation of 1.00 and 1.37. 3H28.3: Watershed output from the swamp subsurface compartment has been in the system 234 times longer than that from the upland surface compartment (14.34 y versus 22.37 d), with a smaller coefficient of variation of 0.97. H29: Except for upland surface water, output of each other compartment has resided for most of its past history in the system within that compartment. 4H29.1: Output water from the upland surface compartment has been in that compartment only 38% of the time since it entered the watershed (8.43 d/22.37 d). 5H29.2: The fractions of past residence times in the watershed that output water from upland subsurface, swamp surface and swamp subsurface compartments have been in those compartments are, respectively, 94% (128.95 d/137.39 d), 96% (130.27 d/136.33 d) and 97% (13.97 y/14.34 y). 6H30: Upland surface water output has been in the upland groundwater compartment 13.94 d (4.18) and in the upland hydrologic subsystem 22.37 d (2.63). 7H31: The past residence time of upland groundwater output is 8.43 d (1.12) in the upland surface compartment and 137.39 d (0.94) in the upland subsystem. H32: Swamp surface water output has the following histories in respect to compartments and subsystems: 8H32.1: Previous time in each other compartment is comparable, and less than several days, but with increasing relative variation downstream and from surface to subsurface: upland surface water 35.92h (3.22), upland groundwater 2.88 d (9.39) and swamp subsurface water 40.30 h (78.35). 9H32.2: Previous time spent as swamp surface water is 130.27 d (1.00). ~°H32.3: Prior time in the upland subsystem has been 4.38 d (6.28) and in the swamp subsystem 131.95 d (1.40). ~H32.4: Prior time as subsurface water has been 4.56 d (29.44) and as surface water 131.77 d (0.99). H33: Swamp subsurface water output has the following past residence time relationships to compartments and subsystems: ~2H33.1: Past time as upland surface water has been 8.32 d (0.99). ~3H33.2: Past time as upland groundwater has been 126.76 d (1.02). ~4H33.3: Previous time spent in the swamp surface compartment has been only 2.26 d (10.69). ~5H33.4: Previous storage as swamp subsurface water has totalled 13.97 y (1.00).

38 t6H33.5: Prior time in the upland subsystem has been 135.09 d (0.96) and in the swamp subsystem 13.97 y (1.00). 17H33.6: Prior time in the surface water subsystem has been only 10.59 d (2.41) and in the subsurface regime 14.32 y (0.98). The following generalizations are embodied in these hypotheses. Water exiting from the swamp subsurface compartment has had a long and relatively invariable history in the watershed, whereas other categories have had relatively short and also invariable past residence times; with the exception of the upland surface water compartment, water leaving a compartment has been in that compartment for most of its history within the system; water exiting from the swamp surface has spent an average of less than several days in each of the other compartments, and is approximately 4 months old in the watershed, on the average; in comparison, water leaving from the swamp subsurface compartment has been in the watershed approximately 14 years. Total residence times The matrix sum ( - - A ' ) - 1 + ( _ A , ) - 1 gives the mean and the matrix V~ the variance of the total residence time in compartment i -- 1..... 4 of water present in c o m p a r t m e n t j -- 1,..., 4 at time t. Table IVc lists these data in the first four rows, with coefficients of variation indicated parenthetically, and again with variable time units for easier interpretation. Data for the subsystems and entire system are presented in the remaining rows. The following conclusions derive from the table. 1H34: Swamp surface water has the shortest and swamp subsurface water the longest expected residence times within the system, 272.04 d (1.20) and 28.32 y (0.02), respectively, the latter with an extremely low coefficient of variation. Upland surface water resides longer and with less variability in the watershed than swamp surface water, 1.51 y (0.64) versus 272.04 d (1.20). Upland groundwater has a fairly long watershed residence time, with the greatest coefficient of variation of any storage category, 2.13 y (2.86). 2H35: The total mean residence times of water in its current compartments is short for upland surface water (16.86 d), longer for upland groundwater (257.91 d) and swamp surface water (260.54 d) and very long and invariant for swamp subsurface water (27.94 y, coefficient of variation 0.02). 3H36: Total time in the swamp surface compartment of water occupying other compartments is short, with decreasing expectations and increasing variability downstream and from surface to bottom: upland surface water 29.42 d (2.80), upland groundwater 4.78 d (7.32) and swamp subsurface water 2.96 d (9.40).

39 H37: Water in each compartment spends less total time in the uplands than in the swamp. 4H37.1: Upland surface water resides 3.2 times longer in the swamp than in the uplands: 1.15 y (0.76) versus 130.41 d (1.07), respectively. 5H37.2: Upland groundwater resides 1.9 times longer in the swamp than in the uplands: 1.39 y (4.35) versus 267.51 d (0.68). 6H37.3: Swamp surface water spends only 4.38 d (6.29) in the uplands versus 61 times longer, 267.66 d (1.22), in the swamp. 7H37.4: Swamp subsurface water resides an average of 135.09 d (0.96) in the upland subsystem versus 27.95 y (0.02), or 76 times longer, in the swamp subsystem. H38: Except for swamp surface water, water in other compartments spends substantially less time in the watershed surface water system than in the subsurface system. 8H38.1: Swamp surface water resides only 10.00 days, with high coefficient of variation (27.09), in subsurface compartments, and 26 times longer with small variation, 262.04 d (0.70), in the surface subsystem. 9H38.2: The total residence time of upland surface water in the surface subsystem is 46.28 d (1.80), and 11 times longer in the subsurface compartments, 1.38 y (0.67). ~°H38.3: The expected total residence time of upland groundwater in surface waters is 14.38 d (2.51), and in subsurface waters 53 times greater, 2.09 y (2.91). 1~H38.4: The total residence time of swamp subsurface water in surface compartments is only 11.28 d (2.57), whereas in subsurface water the time is 915 times longer, 28.28 y (0.02). ~2H39: Surface and subsurface swamp waters exchange very little (as determined by small exchange coefficients a~'3, a~4 and a43, a34 of the matrices A" and A', respectively); this is reflected in short mean residence times, although high coefficients of variation, within each others' compartments: the average molecule of swamp surface water spends only 7.12 d (37.87) in the subsurface compartment, and subsurface water resides only 2.96 d (9.40) in the surface compartment. Those molecules that actually are exchanged remain much longer than average in the destination compartments, however. Generalizations from the preceding hypotheses are as follows. Swamp surface and subsurface waters have the shortest and longest mean residence times, respectively, within the watershed; upland surface water resides for a short period in its current compartment, upland groundwater and swamp surface water moderately longer, and swamp subsurface water for a relatively long time; total time which water in other compartments spends as swamp surface water is short; water spends less time in the upland subsyst

!

40 tem than in the swamp subsystem; except for swamp surface water, water in the other compartments spends less time as surface water than as groundwater; and finally, swamp surface and subsurface waters spend only a few days total time in the other's compartment. DISCUSSION This paper has had the double purpose of demonstrating a new methodology for compartment model analysis, and formulating a concept of the macroscale hydrology of the Okefenokee swamp-upland ecosystem. The capacity of environ analysis to elaborate many diverse relationships within even a simple model has been demonstrated. Therefore, the limiting factor in achieving understanding is not analysis, but modeling itself. The Fig. 5 water balance model is very data limited, relegating to the status of hypotheses the conclusions drawn from its analysis. Despite its deficiencies, the general concept of Okefenokee macrohydrology derived from it is likely to prevail until new, hard to obtain, data appear which challenge its assumptions or quantification. These aspects of the model are examined below by way of qualifying a generalized picture of hydrologic relationships that will then be presented.

Modeling assumptions and quantification Rykiel's (1977, 1982) assumptions of no subsurface input from the deep acquifer, or from the groundwater system outside the surface delimited watershed, were accepted in the process of accepting his Fig. 2 model as the basis for the present work. The approach (Materials section) was then to preserve the quantitative relationships in Fig. 2 while calculating new flows and storages required by the Fig. 5 conceptualization. The qualitative structure of the new model, Rykiel's data and mass balance requirements provided the constraints which limited what the new model could be. The central issues, obviously, are surface-subsurface exchange relationships and upland-swamp interaction. For the latter, fall5] was determined reasonably as a percentage of annual precipitation, leaving a difference f2112]--A115] to be apportioned between f3215] and f4215]. Baseflow, f3215], was then estimated strictly by an assumption that this can only be a boundary phenomenon probably of little significance, and the remainder was allocated by difference to lateral seepage, f4215]. Since f3215] and f4215] lack any factual basis, they represent weak points in the model. The upland surface-subsurface relationship required the following calculations. From the literature, evapotranspiration and infiltration were de-

41 termined to be a fraction of precipitation. Evapotranspiration yl[5], was estimated as the fraction of y~[2] given by the ratio of flooded to unflooded area of the uplands. This is not a strong rationale, but the resultant evapotranspiration value is consistent with literature data and is therefore considered reasonable. Infiltration, f2115], determined by the difference y~[2] -y~[5], is then also reasonable. Transfer from groundwater to surface water, f1215], was calculated by difference to balance compartment 2. Of the other outflows in the balance equation, y~ [5] = y~[2] - y~[5] is reasonable because of the reasonableness of y~[5] established above, and y215] is the same as y212] except for a small balance adjustment; however, f3215] and f4215] were both determined to be weak above, and thus f1215] is also to be considered questionable. The swamp surface-subsurface interaction involved the following computations. The value of f3415] is purely arbitrary based on an assumption of negligible subsurface to surface transfer that has no factual basis, f4315] was determined by difference to balance compartment 3. The inflows z315] and f3115] are sound, but the outflows are less so. Y3115]was derived by partitioning Y2112] into y~[5] and Y4115] based on the ratio of flooded to non-flooded swamp area. This procedure in the uplands gave values similar to literature data, but no such validation is possible here, and Y3115] is considered somewhat in question, y3315] was determined as an arbitrary number from y312] by assuming that baseflow from the swamp, y4315], is small based on documented water retention by peat. This rationale is reasonable, but there is no basis for the actual value of y315], which consequently is also questionable. Therefore, the swamp surface to subsurface transfer f4315] is not a strong number and, since f3415] is arbitrary, the interaction between surface and subsurface swamp water as depicted in Fig. 5 is open to question. Steady state water storage estimates in each of the compartments are considered crude. These are critical to environ analysis as the central matrices ( - A " ) -l and ( - A ' ) -l depend on them (eqs. 6 and 12). To derive these volumes, ratios of flooded to unflooded areas in the uplands and swamp were used in conjunction with average water depths and water holding capacities of different substrates. The area ratios were determined from topographic maps, a reasonable approach. The depths in various categories ({flooded, unflooded} × {uplands, swamp}) are arbitrary, but based on general experience in the region. Field capacities from the literature are probably representative of regional substrates. The total swamp storage, x~' + x] =- 3.6368 × 10 9 m 3 in Fig. 5, is greater than the 1.682 × 10 9 m 3 value shown in Fig. 2 because a shallower depth was used to calculate the subsurface component in the latter case. Otherwise, the two values would agree closely. As a group, the storage estimates of the model are probably reasonable, although refinements would be desirable.

42 In summary, of seven internal flows in the Fig. 5 model, only two of them, f3115] and f2115], have acceptable factual standing for the purpose of drawing firm conclusions from the environ analysis. In defense, the difficulties of measuring the surface-subsurface flows f1215], f4315] and f3415], and the upland-swamp flows f32[5] and f42 [5], are obvious. These flows are critical to any subsequent improvement of the state of knowledge of Okefenokee water relationships, given the validity of underlying assumptions about lack of subsurface inputs from outside the watershed boundary. Storage estimates are probably reasonable, but should be improved as possible. With these qualifications, a tentative general concept of Okefenokee macrohydrology can be formulated based on the environ analysis.

Generalized concept of Okefenokee macrohydrology Figure 5 depicts the following general scheme of water relationships in the watershed. Upland precipitation is routed mainly to groundwater and then out of the system by evapotranspiration. Swamp precipitation remains in the surface compartment to exit the watershed by evapotranspiration and streamflow. Upland groundwater that remains within the system is mainly returned to the upland streams where it, together with surface water, is transported to the swamp surface compartment. Upland groundwater appears to contribute significantly to swamp subsurface water, which forms the largest storage pool within the watershed. From the magnitudes of the two main flows that couple the swamp and uplands, f3~ and f42, it cannot be determined whether these linkages are relatively weak or relatively strong. Assuming they are weak to moderate, the following general picture of the watershed's hydrologic organization emerges ( ~ , strong interaction; . . . . , moderate interaction). Z1

Z3

x~'. . . . . ,-x~' ~Y3 4', Y2

<-~ Y ~ -

"~2

....

>.,v-~ -->

"~4

(17)

):4

According to this concept, the system consists of three relatively discrete subsystems, uplands, swamp surface and swamp subsurface, the last two essentially decoupled from each other but weakly coupled to the first. Assessment of the relative strengths of the coupling flows f3~ and f42 is aided by referring to the system's environs. The unit output environs (Fig. 6) essentially confirm the description derived from Fig. 5. They show, for example, the negligible coupling of swamp surface and subsurface, and of upland groundwater to swamp surface water. E~' also indicates that per unit

43 of upland precipitation the flow f3~ is moderate whereas f42 is relatively weak. The unit input environs E~ and E~ (Fig. 7) verify the left side of (17), showing the upland subsurface to surface coupling to be relatively weak per unit surface output, but the surface to subsurface linkage relatively strong per unit of groundwater output. E~ and E~ verify the negligible coupling of upland groundwater to the swamp surface. E~ further shows f31 to be moderate and f42 relatively weak per unit of swamp surface output. E~ indicates f31 to be negligible but f42 to be very strong per unit of swamp subsurface output. Thus, based on the relationships exhibited within environs, the concept represented in (17) should be modified as follows: Z1

....

Z3

x -+y3

(18)

Y2 ~ X~'------'~ X~ -* Y4

This scheme indicates t h e Okefenokee watershed to be hydrologically organized into two relatively discrete subsystems, upland surface-watershed subsurface and swamp surface, with strong input-output coupling within each but only moderate coupling between them provided by upland surface flows. Further, more detailed substantiation of this generalized concept can be sought in specific relationships of the conclusions of the Results section.

Surface-subsurface interactions The hydrologic organization represented by (18) postulates that (1) swamp surface-subsurface interaction (f43, f34) is negligible, (2) the flow from upland groundwater to swamp surface (f32) is negligible, (3) transfer of water from upland surface to upland groundwater (f21) is a strong linkage and (4) the reverse upland transfer from groundwater to surface water (f12) is a coupling of only moderate strength. The Results section's conclusions pertaining to each of these postulates are as follows.

Swamp surface-subsurface interaction That exchange between swamp surface and subsurface water is negligible is reflected in the following relationships. Only 0.04% of swamp precipitation leaves the watershed as output from the subsurface compartment (H2). The composition of subsurface output is 99% upland precipitation and only 1% swamp precipitation (H2.2, H6.2). One unit of upland precipitation generates 1.29 units of intrasystem flow, whereas a unit of swamp precipitation generates only 0.001 units of internal flow (H7.1). Less than 0.09% of the total intrasystem flow is of swamp precipitation origin; it virtually all

44

originates with upland precipitation (H7.2). One unit of upland precipitation generates only 0.0002 units o f f43, and only 0.0004 units o f f 3 4 ( H 8 , H9.1). One unit of swamp precipitation generates 0.0011 units of f43, and only 0.000006 units off34 (H9.1). The composition of f34 is 99% upland precipitation and only 1% swamp precipitation (H9.3). The number of future intercompartmental transfers for swamp surface water is only 0.001, and for subsurface water 0.006 (Hl l.1). The number of future and past cycles of water in compartments 3 and 4 is only 10 -5 (Hl l.2, Hl l.5). Only 4% of swamp subsurface storage, which has an extremely long future residence time of 13.97 y (H21.3), has its origin in swamp precipitation (H14, H16). Swamp surface water output consists of only 1% swamp subsurface water (H18.3), and subsurface output consists of only 0.04% swamp surface water (H18.4). Only 0.1% of swamp surface storage will exit the watershed as swamp subsurface output (H19.3), and only 0.5% of subsurface storage will leave as swamp surface output. Swamp precipitation will reside only 5.44 d in the subsurface compartment (24.4) versus a watershed future residence time of 135.71 d (H20). Swamp surface water spends 96% of its future residence time within the system in the swamp surface compartment, * and swamp subsurface water spends virtually 100% of its future in the subsurface compartment (H27). Water leaving the system from the swamp surface, which has been there 130.27 d (Table IVa), has been in the subsurface compartment only 40.30 h (H32.1), and in the watershed subsurface subsystem only 4.56 d (H32.4). Water present in or exiting the system from the swamp subsurface,, which has been there 13.97 y (Table IVb), has spent only 2.26 d in the swamp surface (H33.3) and only 10.59 d in the watershed surface subsystem (H33.6). The total residence time of swamp surface water in the subsurface subsystem is 10.00 d (H38.1), and in the swamp subsurface compartment only 7.12 d (H39). The total residence time of swamp subsurface water in the watershed surface subsystem is 11.28 d (H38.4), and in the swamp surface compartment only 2.96 d (H39). By these many expressions of the kinetics established by the low exchange fluxes, f43 and f34, in the Fig. 5 model, the following is concluded: Postulate 1. Surface-subsurface interchange of water in Okefenokee Swamp is of negligible significance, and the swamp surface water is effectively decoupled from underlying subsurface water. * The following coincidence is noteworthy. Rykiel (1977, p. i 19), by a totally unrelated procedure, computed the 'residence time' of swamp surface water to be 130 d. It is clear he was computing a future residence time because he spoke in terms of the need for renewal every few months, and of surface water as the source of streamflow. The present environ analysis gives a future residence time of swamp surface water within the swamp surface compartment as 130.27 d (H24.2).

45

Swamp surface-upland groundwater interaction The following observations are pertinent to evaluating the status of the upland groundwater contribution to swamp surface water. Only 0.4% of upland precipitation is routed directly to compartment 3 via compartment 2; that is, one unit of upland precipitation generates 0.2 units of intrasystem outflows from upland groundwater (H8), of which only 2% is transferred by f32 to swamp surface water (H8.2). Output from the swamp surface compartment consists of only 2% upland groundwater (H 18.3), most of which arrives by the path fl2, f3~ rather than f32 (Figs. 5, 6). Output from the swamp surface compartment has spent a total time of only 4.38 d in both upland compartments (H32.3), and only 4.56 d in both subsurface compartments (H32.4): therefore, total contact with compartment 2 has to have been small. Accordingly, the following is justified. Postulate 2. The baseflow contribution of upland groundwater to swamp surface water is small, this interaction being stronger than the swamp surface-subsurface linkage, but still basically negligible in the overall watershed hydrology.

Upland surface-subsurface transfer Relationships which bear on interpreting the flow from upland surface to groundwater as a strong interaction are as follows. Sixty-three percent of upland precipitation leaves the system as upland groundwater evapotranspiration; this is derived as the fraction of upland precipitation lost as watershed evapotranspiration (83%, H1) which represents evapotranspiration from the groundwater compartment (76%, HI.1). Of upland precipitation transferred internally, 80% goes from upland surface to groundwater (H8.1). Most watershed storage is in the subsurface compartments (Fig. 5); one unit of upland precipitation generates 1.45 units of watershed storage compared to only 0.37 units generated by each unit of swamp precipitation (H12). Of total watershed storage which originates as upland precipitation, 19% occurs in compartment 2 (H13). Upland surface output consists of 62% groundwater (H 18.1), signifying strong prior infiltration. Sixty-six percent of upland surface storage leaves the watershed as output from the groundwater compartment (H19.1). Upland surface output has resided in compartment 2 13.94 d of a total past in the uplands of 22.37 d (H30). Swamp subsurface storage or output has a past residence time of only 8.32 d in compartment 1 (H33.1), and flow from 1 to 4 via 3 is negligible. The total residence time of upland groundwater in the upland surface compartment is only 4.78 d (H36), indicating rapid transfer to groundwater from surface water. These characteristics support the next conclusion. Postulate 3. The infiltration of surface water into the groundwater of the

46 sandy soil uplands constitutes strong hydrologic coupling of the upland compartments.

Upland subsurface-surface transfer That subsurface to surface flow in the uplands represents a linkage of only moderate strength is supported by the following indications. One unit of upland precipitation generates 0.2 units of intrasystem outflows (H8), of which 60% (H8.2), representing 12% of precipitation, is returned to the upland surface water compartment. In the cycler21, f12, the number of future and past intercompartmental transfers is low, 0.12 (H 11.2, H 11.5), indicating a relatively weak return from groundwater to surface water. However, evapotranspiration from the upland surface consists of 62% groundwater (H 18.1), suggesting a relatively strong return to compartment 1. The problem is different levels of storage in the two compartments, which results in a high subsurface component in upland surface output. In reality, only 0.46% of subsurface storage will leave the watershed as upland surface output (H19.2), indicating only moderate strength for f~2 in view of the strong tendency in f2~ of surface water to return to groundwater, That water leaving the system from compartment 1 has spent only 38% of its watershed past in that compartment (H29.1) is strongly indicative of relatively strong baseflow. Similarly, of a total past residence time of 22.37 d in the upland compartments, water exiting the system from compartment 1 has been in compartment 2 for a total of 13.94 d (H30). Swamp surface water storage or output has spent only 2.88 d in compartment 2 (H32.2), indicating, since f3z is negligible, that the path f2~, f32, of which upland baseflow is a component, is weak. The total residence time of upland subsurface water in the surface subsystem of the watershed is 14.38 d (H38.3), indicating moderate return via f2 ~ since f32 is weak. Thus, while interpretation is difficult due to differing pool sizes in compartments 1 and 2, the preponderant weight of these observations supports the following conclusion. Postulate 4. Baseflow from upland subsurface to surface water represents a coupling between these compartments that is neither very strong nor very weak, but moderate in strength. In summary, concerning watershed surface-subsurface relationships, the upland subsystem is strongly linked from surface to subsurface and only moderately linked in the reverse direction. The swamp surface and subsurface compartments are essentially decoupled from significant interaction. The situation is therefore as depicted in (18).

Upland-swamp interactions The hydrologic regime as represented in (18) postulates that (1) the transfer of upland groundwater to swamp subsurface water (f32) constitutes

47 a strong coupling, whereas (2) that from upland surface to swamp surface is a linkage of only moderate strength. The relationships pertinent to these conclusions are as follows.

Upland-swamp subsurface interaction The subsurface transfer of water from uplands to swamp is considered strong in view of the following observations. Fifty-one percent of upland precipitation exits the watershed as swamp subsurface water (H2.1). Swamp subsurface output and storage consist of 99% upland precipitation (H3.3, H6.2, H16). One unit of upland precipitation generates 0.2 units of intrasystem outflows from compartment 2 (H8), of which 38%, representing 8% of upland precipitation, is transferred to swamp subsurface storage (H8.2). The small amount of water transferred from swamp subsurface to surface consists of 99% upland precipitation (H9.3). Of the total storage of upland precipitation within the watershed, 74% is in the swamp subsurface compartment (H13). Nine percent of upland surface water and 10% of upland groundwater will leave the watershed as swamp subsurface water output (H19.1, H19,2). Upland groundwater will spend 80% of its future residence time within the system in other compartments than 2 (H27). Swamp subsurface output has spent 126.76 d in compartment 2 (H33.2) which, in view of the long history of 13.97 y in compartment 4, indicates relatively quick (strong) transfer from upland groundwater to swamp subsurface water. Swamp subsurface water spends 76-fold less time in the uplands than in the swamp (H37.4). Swamp subsurface water resides 915 times longer in the watershed subsurface subsystem than in the surface subsystem (H38.4), indicating relatively rapid transfer to compartment 4 over the path fzl, f42 since the swamp surface-subsurface exchange is negligible. Thus, the following conclusion is justified. Postulate 5. The transfer of upland groundwater to swamp subsurface water represents strong linkage which, combined with the strong surface to subsurface coupling between upland compartments, results in a strongly interconnected subsystem consisting of the three compartments upland surface water, upland groundwater and swamp subsurface water.

Upland-swamp surface interaction The streamflow and overland flow connection between the upland and swamp surface compartments is only moderate in strength, as the following relationships signify. Of the 83% of upland precipitation lost from the watershed as evapotranspiration (H 1), 15 % is swamp surface evapotranspiration (HI.1), giving 12.5% of upland input leaving the system by this means. Of the 11% of upland precipitation that exits as streamflow (H3), 95% is swamp surface streamflow (H3.1), so that 10.5% of upland precipitation

48

leaves the watershed as streamflow generated by compartment 3. Accordingly, only 23% of upland precipitation is lost from the system as swamp surface output (H19.1). Also, only 18% of swamp surface storage is composed of water that originated as upland precipitation (H6.1, H15). Of upland precipitation transferred internally, only 20% goes to swamp surface water whereas 80% goes to upland groundwater (H8.1). Only 16% of swamp surface to subsurface water is of upland precipitation origin (H9.2). Only 6% of upland precipitation stored in the watershed is stored in compartment 3 (H13). Output of swamp surface water consists of only 1% upland surface water (H18.3). Swamp surface output has a past residence time in compartment 1 of only 35.92 h (H32.2) suggesting rapid transfer; but the quantities are small due to differential storages (Fig. 5) so that the interaction is not relatively strong. Similarly, total residence time of swamp surface water in the upland surface compartment is only 2.96 d (H36). The following conclusion is supported. Postulate 6. The transfer of upland surface water to the swamp surface compartment is a linkage that is only moderate in strength. Therefore, the swamp surface compartment is a relatively distinct subsystem hydrologically from the remaining watershed compartments. CONCLUSION

The generalized concept of water relations in the Okefenokee watershed schematized in (18) is supported by environ analysis of the Fig. 5 model. Within the model's limitations, already expressed, it is possible to conclude the following about the macrohydrologic organization of the swamp-upland complex. There are two relatively discrete subsystems within the watershed. One is the surface water compartment of the swamp proper. The other consists of the three upland surface-watershed subsurface compartments. These subsystems are each strongly connected within, but only moderately connected between by virtue of surface flows off the uplands and into the swamp. This general conception, together with the specific conclusions of the results, with which it is consistent, may now be adopted qualifiedly to guide management activities and also future research on water relations of the unique and important natural heritage that is the Okefenokee Swamp ecosystem. REFERENCES Barber, M.C., 1978a. A retrospective Markovian model for ecosystem resource flow. Ecol. Modelling, 5: 125-135.

49 Barber, M.C., 1978b. A Markovian model for ecosystem flow analysis. Ecol. Modelling, 5: 193-206. Barber, M.C., 1979. A note concerning time parameterization of Markovian models of ecosystem flow analysis. Ecol. Modelling, 6: 323-328. Barber, M.C., Patten, B.C. and Finn, J.T., 1979. Review and evaluation of input-output flow analysis for ecological applications. In: J.H. Matis, B.C. Patten and G.C. White (Editors), Compartmental Analysis of Ecosystem Models, Vol. S-10. Statistical Ecology Satellite Program Proceedings, Parma, Italy. Internatl. Stat. Ecol. Program, International Cooperative Publishing House, Fairland, MD. Blood, E.R., 1981. Surface water hydrology and biogeochemistry of the Okefenokee Swamp watershed. Ph.D. Dissertation, University of Georgia, Athens, GA. Callahan, J.T., 1964. The yield of sedimentary aquifers of the coastal plain southeast river basins. Geol. Surv. Water Supply Paper 1669-W. U.S. Government Printing Office, Washington, DC. Cohen, A.D., 1973. Possible influences of subpeat topography and sediment type upon the development of the Okefenokee swamp-marsh complex of Georgia. Southeast. Geol., 15: 141-151. Finn, J.T., 1976. Measures of ecosystem structure and function derived from analysis of flows. J. Theor. Biol., 56: 363-380. Finn, J.T., 1977. Flow analysis: a method for analyzing flows in ecosystems. Ph.D. Dissertation, University of Georgia, Athens, GA. Finn, J.T., 1978. Cycling index: a general definition for cycling in compartment models. In: D.C. Adriano and I.L. Brisbin (Editors), Environmental Chemistry and Cycling Processes Symposium. U.S. Energy Research and Development Administration, Washington, DC. Finn, J.T. and Rykiel, E.J., 1979. Effect of the Suwannee River Sill on Okefenokee Swamp water level. Water Resour. Res., 15: 313-320. Hamilton, D.B., 1981. Plant succession and the influence of disturbance in the Okefenokee Swamp, Georgia. Ph.D. Dissertation, University of Georgia, Athens, GA. Hannon, B., 1973. The structure of ecosystems. J. Theor. Biol., 41: 535-546. Hopkins, J.M., 1947. Forty-five years with the Okefenokee Swamp. Ga. Soc. Nat. Bull., 4: 1-75.

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